Scaling metabolic rate fluctuations

Peto's "Paradox" and Six Degrees of Cancer Prevalence

Peto's paradox and the epidemiologic observation of the average six degrees of tumor prevalence are studied and hypothetically solved. A simple consideration, Petho's paradox challenges our intuitive understanding of cancer risk and prevalence. Our simple consideration is that the more a cell divides, the higher the chance of acquiring cancerous mutations, and so the larger or longer-lived organisms have more cells and undergo more cell divisions over their lifetime, expecting to have a higher risk of developing cancer. Paradoxically, it is not supported by the observations. The allometric scaling of species could answer the Peto paradox. Another paradoxical human epidemiology observation in six average mutations is necessary for cancer prevalence, despite the random expectations of the tumor causes. To solve this challenge, game theory could be applied. The inherited and random DNA mutations in the replication process nonlinearly drive cancer development. The statistical variance concept does not reasonably describe tumor development. Instead, the Darwinian natural selection principle is applied. The mutations in the healthy organism's cellular population can serve the species' evolutionary adaptation by the selective pressure of the circumstances. Still, some cells collect multiple uncorrected mutations, adapt to the extreme stress in the stromal environment, and develop subclinical phases of cancer in the individual. This process needs extensive subsequent DNA replications to heritage and collect additional mutations, which are only marginal alone. Still, together, they are preparing for the first stage of the precancerous condition. In the second stage, when one of the caretaker genes is accidentally mutated, the caused genetic instability prepares the cell to fight for its survival and avoid apoptosis. This can be described as a competitive game. In the third stage, the precancerous cell develops uncontrolled proliferation with the damaged gatekeeper gene and forces the new game strategy with binary cooperation with stromal cells for alimentation. In the fourth stage, the starving conditions cause a game change again, starting a cooperative game, where the malignant cells cooperate and force the cooperation of the stromal host, too. In the fifth stage, the resetting of homeostasis finishes the subclinical stage, and in the fifth stage, the clinical phase starts. The prevention of the development of mutated cells is more complex than averting exposure to mutagens from the environment throughout the organism's lifetime. Mutagenic exposure can increase the otherwise random imperfect DNA reproduction, increasing the likelihood of cancer development, but mutations exist. Toxic exposure is more challenging; it may select the tolerant cells on this particular toxic stress, so these mutations have more facility to avoid apoptosis in otherwise collected random mutational states.

A general theory for temperature dependence in biology

At present, there is no simple, first principles-based, and general model for quantitatively describing the full range of observed biological temperature responses. Here we derive a general theory for temperature dependence in biology based on Eyring-Evans-Polanyi's theory for chemical reaction rates. Assuming only that the conformational entropy of molecules changes with temperature, we derive a theory for the temperature dependence of enzyme reaction rates which takes the form of an exponential function modified by a power law and that describes the characteristic asymmetric curved temperature response. Based on a few additional principles, our model can be used to predict the temperature response above the enzyme level, thus spanning quantum to classical scales. Our theory provides an analytical description for the shape of temperature response curves and demonstrates its generality by showing the convergence of all temperature dependence responses onto universal relationships-a universal data collapse-under appropriate normalization and by identifying a general optimal temperature, around 25 ^∘C, characterizing all temperature response curves. The model provides a good fit to empirical data for a wide variety of biological rates, times, and steady-state quantities, from molecular to ecological scales and across multiple taxonomic groups (from viruses to mammals). This theory provides a simple framework to understand and predict the impact of temperature on biological quantities based on the first principles of thermodynamics, bridging quantum to classical scales.

Comparison of Metabolic Rates of Young of the Year Beluga (Huso huso), Sterlet (Acipenser ruthenus) and Bester Hybrid Reared in a Recirculating Aquaculture System

In the present study, oxygen consumption of two sturgeon species, beluga (Huso huso), sterlet (Acipenser ruthenus), and their hybrid reared in a recirculating aquaculture system were compared over body intervals from 54–107 g to determine the interspecific variation of metabolic rate. Metabolic rates were measured using the intermittent-flow respirometry technique. Standard oxygen consumption rates (SMR, mg O2 h−1) of sterlet were 30% higher compared with beluga and 22% higher compared with bester hybrid. The routine metabolic rate (RMR, mg O2 h−1) averaged 1.58 ± 0.13 times the SMR for A. ruthenus, 1.59 ± 0.3 for H. huso, and 1.42 ± 0.15 for the hybrid bester. However, the study revealed no significant differences (p > 0.05) between mean values of SMR and RMR for beluga and bester hybrid. The scaling coefficient reflected a closed isometry for the hybrid (b = 0.97), while for the purebred species the coefficient of 0.8 suggests a reduction in oxygen consumption with increasing body mass. These findings may contribute to understanding the differences in growth performances and oxygen requirements of the studied species reared in intensive aquaculture system.

Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids

Allometric scaling has many applications, from the prediction of pharmacokinetics in animals and humans to the probing of ecosystem dynamics. Most studies have neglected to account for variations and fluctuations, although they are intrinsic features of all biological systems. To understand how metabolic scaling emerges in the presence of variations, we developed computer-generated models of cell-laden spheroids to define the experimental size range of cell cultures with quantifiable similitudes in terms of fluctuations and metabolic scaling with living organisms. We show that the estimates of scaling exponents may change with increasing variability in both mass and metabolic rate. The computational pipeline described underpins the sound design of statistically meaningful cell-based models, with impacts in both biomedical science and ecology.

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m⁻³) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

Dynamic metabolic adaptation can promote species coexistence in competitive microbial communities

Microbes are capable of physiologically adapting to diverse environmental conditions by differentially varying the rates at which they uptake different nutrients. In particular, microbes can switch hierarchically between different energy sources, consuming first those that ensure the highest growth rate. Experimentally, this can result in biphasic growth curves called "diauxic shifts" that typically arise when microbes are grown in media containing several nutrients. Despite these observations are well known in microbiology and molecular biology, the mathematical models generally used to describe the population dynamics of microbial communities do not account for dynamic metabolic adaptation, thus implicitly assuming that microbes cannot switch dynamically from one resource to another. Here, we introduce dynamic metabolic adaptation in the framework of consumer-resource models, which are commonly used to describe competitive microbial communities, allowing each species to temporally change its preferred energy source to maximize its own relative fitness. We show that dynamic metabolic adaptation enables the community to self-organize, allowing several species to coexist even in the presence of few resources, and to respond optimally to a time-dependent environment, thus showing that dynamic metabolic adaptation could be an important mechanism for maintaining high levels of diversity even in environments with few energy sources. We show that introducing dynamic metabolic strategies in consumer-resource models is necessary for reproducing experimental growth curves of the baker's yeast Saccharomyces cerevisiae growing in the presence of two carbon sources. Even though diauxic shifts emerge naturally from the model when two resources are qualitatively very different, the model predicts that the existence of such shifts is not a prerequisite for species coexistence in competitive communities.

Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton

Kleiber's law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber's law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber's law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber's law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

The roles of metabolic thermogenesis in body fat regulation in striped hamsters fed high-fat diet at different temperatures

The metabolic thermogenesis plays important roles in thermoregulation, and it may be also involved in body fat regulation. The thermogenesis of brown adipose tissue (BAT) is largely affected by ambient temperature, but it is unclear if the roles in body fat regulation are dependent on the temperature. In the present study, uncoupling protein 1 (ucp1)-based BAT thermogenesis, energy budget and body fat content were examined in the striped hamsters fed high fat diet (HF) at cold (5°C) and warm (30°C) temperatures. The effect of 2, 4-dinitrophenol (DNP), a chemical uncoupler, on body fat was also examined. The striped hamsters showed a notable increase in body fat following the HF feeding at 21°C. The increased body fat was markedly elevated at 30°C, but was significantly attenuated at 5°C compared to that at 21°C. The hamsters significantly increased energy intake at 5°C, but consumed less food at 30°C relative to those at 21°C. Metabolic thermogenesis, indicated by basal metabolic rate, UCP1 expression and/or serum triiodothyronine levels, significantly increased at 5°C, but decreased at 30°C compared to that at 21°C. A significant decrease in body fat content was observed in DNP-treated hamsters relative to the controls. These findings suggest that the roles of metabolic thermogenesis in body fat regulation largely depend on ambient temperature. The cold-induced enhancement of BAT thermogenesis may contribute the decreased body fat, resulting in a lean mass. Instead, the attenuation of BAT thermogenesis at the warm may result in notable obesity.

Community fluctuations and local extinction in a planktonic food web

Determining statistical patterns irrespective of interacting agents (i.e. macroecology) is useful to explore the mechanisms driving population fluctuations and extinctions in natural food webs. Here, we tested four predictions of a neutral model on the distribution of community fluctuations (CF) and the distributions of persistence times (APT). Novel predictions for the food web were generated by combining (1) body size-density scaling, (2) Taylor's law and (3) low efficiency of trophic transference. Predictions were evaluated on an exceptional data set of plankton with 15 years of weekly samples encompassing c. 250 planktonic species from three trophic levels, sampled in the western English Channel. Highly symmetric non-Gaussian distributions of CF support zero-sum dynamics. Variability in CF decreased while a change from an exponential to a power law distribution of APT from basal to upper trophic positions was detected. Results suggest a predictable but profound effect of trophic position on fluctuations and extinction in natural communities.

Studying the evolutionary significance of thermal adaptation in ectotherms: The diversification of amphibians' energetics

A fundamental problem in evolutionary biology is the understanding of the factors that promote or constrain adaptive evolution, and assessing the role of natural selection in this process. Here, comparative phylogenetics, that is, using phylogenetic information and traits to infer evolutionary processes has been a major paradigm . In this study, we discuss Ornstein-Uhlenbeck models (OU) in the context of thermal adaptation in ectotherms. We specifically applied this approach to study amphibians's evolution and energy metabolism. It has been hypothesized that amphibians exploit adaptive zones characterized by low energy expenditure, which generate specific predictions in terms of the patterns of diversification in standard metabolic rate (SMR). We complied whole-animal metabolic rates for 122 species of amphibians, and adjusted several models of diversification. According to the adaptive zone hypothesis, we expected: (1) to find "accelerated evolution" in SMR (i.e., diversification above Brownian Motion expectations, BM), (2) that a model assuming evolutionary optima (i.e., an OU model) fits better than a white-noise model and (3) that a model assuming multiple optima (according to the three amphibians's orders) fits better than a model assuming a single optimum. As predicted, we found that the diversification of SMR occurred most of the time, above BM expectations. Also, we found that a model assuming an optimum explained the data in a better way than a white-noise model. However, we did not find evidence that an OU model with multiple optima fits the data better, suggesting a single optimum in SMR for Anura, Caudata and Gymnophiona. These results show how comparative phylogenetics could be applied for testing adaptive hypotheses regarding history and physiological performance in ectotherms.

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r(VO₂), in the laboratory mouse Mus musculus, assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO₂) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 10² s), either monofractal or weak multifractal dynamics are observed depending on whether T_a < 15 °C or T_a > 15 °C respectively. For larger time scales, r(VO₂) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ(q), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b. We also show that the long-range correlation structure of r(VO₂) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system.

Ecological and scaling analysis of the energy expenditure of rest, activity, flight, and evaporative water loss in Passeriformes and non-Passeriformes in relation to seasonal migrations and to the occupation of boreal stations in high and moderate latitudes

A unified system of bioenergetic parameters that describe thermal regulation and energy metabolism in many passerine and non-passerine species has been developed. These parameters have been analyzed as functions of ambient temperature, and bioenergetic models for various species have been developed. The level of maximum food energy or maximal existence metabolism (MPE) is 1.3 times higher in passerines than in non-passerines, which is consistent with the ratio of their basal metabolic rates (BMR). The optimal ambient temperature for maximizing productive processes (e.g., reproduction, molting) is lower for passerines than for non passerines, which allows passerines to have higher production rates at moderate ambient temperatures. This difference in the optimal ambient temperature may explain the variation in bioenergetic parameters along latitudinal gradients, such as the well-known ecological rule of clutch size (or mass) increase in the more northerly passerine birds. The increased potential for productive energy output in the north may also allow birds to molt faster there. This phenomenon allows passerine birds to occupy a habitat that fluctuates widely in ambient temperature compared with non-passerine birds of similar size. Passerines have a more effective system for maintaining heat balance at both high and low temperatures. The high metabolism and small body sizes of passerines are consistent with omnivore development and with ecological plasticity. Among large passerines, the unfavorable ratio of MPE to BMR should decrease the energy that is available for productive processes. This consequence limits both the reproductive output and the development of long migration (particularly in Corvus corax). The hypothesis regarding BMR increase in passerines was suggested based on an aerodynamic analysis of the flight speed and the wing characteristics. This allometric analysis shows that the flight velocity is approximately 20% lower in Passeriformes than in non-Passeriformes, which is consistent with the inverted ratio of their BMR level. The regressions for the aerodynamic characteristics of wings show that passerines do not change the morphological characteristics of their wings to decrease velocity. Passerine birds prefer forest habitats. The size range of 5-150 g for birds in forest habitats is almost exclusively occupied by passerines because of their large energetic capability.

Scaling body size fluctuations

The size of an organism matters for its metabolic, growth, mortality, and other vital rates. Scale-free community size spectra (i.e., size distributions regardless of species) are routinely observed in natural ecosystems and are the product of intra- and interspecies regulation of the relative abundance of organisms of different sizes. Intra- and interspecies distributions of body sizes are thus major determinants of ecosystems' structure and function. We show experimentally that single-species mass distributions of unicellular eukaryotes covering different phyla exhibit both characteristic sizes and universal features over more than four orders of magnitude in mass. Remarkably, we find that the mean size of a species is sufficient to characterize its size distribution fully and that the latter has a universal form across all species. We show that an analytical physiological model accounts for the observed universality, which can be synthesized in a log-normal form for the intraspecies size distributions. We also propose how ecological and physiological processes should interact to produce scale-invariant community size spectra and discuss the implications of our results on allometric scaling laws involving body mass.

Comparative basal metabolic rate among passerines and the food habit hypothesis

The food habit hypothesis (FHH) predicts that mass-independent BMR is associated with dietary traits. In spite of decades of research, the FHH remains controversial, in part because ambiguities surrounding diet categorization can potentially confound interpretations from interspecific analyses of the relative importance of diet quality. In this study, we investigated possible relationships between BMR and the percentage of nitrogen, and the percentage of various prey items in the gut content of 19 passerine species under an explicit phylogenetic context. There were no significant effects of the percentage of dietary nitrogen, invertebrates, or plants on mass-independent BMR using either conventional or phylogenetically corrected regressions. Consequently, our results do not support the FHH in passerine birds. The lack of a significant correlation between diet and BMR could be explained by generally similar levels of activity and similar body composition among species. In this sense, it is possible that the impact of food habits could depend mainly on body mass, which is also associated to the high cost of the endothermy at small sizes.