Kleiber's Law Research Articles

High-Precision Calorimetry-Based Analysis of Pupal-Pharate Adult Development in Drosophila melanogaster.

In holometabolous insects, the larval body is almost completely decomposed and reconstructed into the adult body during the pupal-pharate adult stages. Therefore, the total energetic cost of this process is a key thermodynamic quantity necessary for evaluating the benefit of their life history. Here, we measured whole-body thermal dissipation of single pupae of the fruit fly, Drosophila melanogaster, during the period from puparium formation to adult eclosion as a function of age, using a high-precision isothermal calorimeter at T = 298 K. The mass-specific energy consumption during the period from the onset of larval-pupal apolysis to adult eclosion was determined to be 2.3 kJ/g for an individual of mass (adult) = 1.0 mg, while it was observed to follow Kleiber's law for individuals smaller than mass (adult) = 1.0 mg. During the pupal-pharate adult period, in addition to the U-shaped variation, several characteristic thermal dissipations related to various events, including somatic muscle contractions, ecdyses, pulsatile hormone secretion in a pharate adult, and vaporization of the exuvial fluid, were observed. The periodic bursts in the pharate adult stage grew exponentially, suggesting that the positive feedback in the metabolic system synchronized with the progression of development, making the energy consumption in this stage more efficient. The present study showed that high-precision calorimetry is a powerful and credible method for measuring not only the total energy spent during development but also the energy spent during every specific developmental event in an organism.

A Nonlinear Dynamical View of Kleiber's Law on the Metabolism of Plants and Animals.

Kleiber's empirical law, which describes that metabolism increases as the mass to the power 3/4, has arguably remained life sciences' enigma since its formal uncovering in 1930. Why is this behavior sustained over many orders of magnitude? There have been quantitative rationalizations put forward for both plants and animals based on realistic mechanisms. However, universality in scaling laws of this kind, like in critical phenomena, has not yet received substantiation. Here, we provide an account, with quantitative reproduction of the available data, of the metabolism for these two biology kingdoms by means of broad arguments based on statistical mechanics and nonlinear dynamics. We consider iterated renormalization group (RG) fixed-point maps that are associated with an extensive generalized (Tsallis) entropy. We find two unique universality classes that satisfy the 3/4 power law. One corresponds to preferential attachment processes-rich gets richer-and the other to critical processes that suppress the effort for motion. We discuss and generalize our findings to other empirical laws that exhibit similar situations, using data based on general but different concepts that form a conjugate pair that gives rise to the same power-law exponents.

Comparing the spreading characteristics of monkeypox (MPX) and COVID-19: Insights from a quantitative model

Climate change is acknowledged to directly affect not only the environment, economy, and society but also the transmission dynamics of infectious diseases, thereby impacting public health.The recent experiences with the spread of SARS-CoV-2 and Monkeypox have highlighted the complex and interconnected nature of infectious diseases, which are strongly linked to various determinants of health. Considering these challenges, adopting a new vision such as the trans-disciplinary approach appears to be imperative.This paper proposes a new theory about viruses' spread, based on a biological model, accounting for the optimisation of energy and material resources for organisms' survival and reproduction in the environment. The approach applies Kleiber's law scaling theory, originally developed in biology, to model community dynamics in cities. A simple equation can be used to model pathogen spread without accounting for each species' physiology by leveraging the superlinear scaling of variables with population size. This general theory offers several advantages, including the ability to explain the rapid and surprising spread of both SARS-CoV-2 and Monkeypox. The proposed model shows similarities in the spreading processes of both viruses, based on the resulting scaling factors, and opens new avenues for research.By fostering cooperation and integrating knowledge from different disciplines to effectively tackle the multifaceted dimensions of disease outbreaks, we can work towards preventing future health emergencies.

Abstract P1034: Neurohormonal Pathways Drive Postnatal Thermogenesis And Loss Of Cardiac Regenerative Potential

Why do mammalian organs including the heart lose regenerative potential during the perinatal window remains enigmatic. Through phylogenetic analysis of vertebrate cardiomyocyte ploidy as a proxy for cardiac regenerative potential, we uncover that certain monotreme, edentate, cetacean, chiropteran species have unusually high percentages of diploid cardiomyocytes in the adult heart. Cardiomyocyte abundance across 41 vertebrate species conforms to Kleiber's law, the 3/4-power law scaling of metabolism with bodyweight, and decreases when the standard metabolic rate and body temperature increase during the ectotherm-to-endotherm transition. Recently, following the fractal feature of the cardiovascular system, we further strengthen the link between endothermy and heart physiology. Thermogenesis increases by more than 10-fold during the ectotherm-to-endotherm transition requiring similar increases in blood flow and cardiac function that may impede heart regenerative potential. Moreover, we report sympathetic nerve-adrenergic receptor and thyroid hormone signaling as two major pathways promoting both thermogenesis and cardiomyocyte cell cycle arrest. Combined inhibition of postnatal adrenergic and thyroid hormone signaling results in juvenile mice with strikingly low body temperatures (~25 ° C), significantly elevated abundances of diploid cardiomyocytes (~60%), dramatically increased cardiomyocyte proliferation, and enhanced cardiac regenerative abilities when analyzed at postnatal day 14. Intriguingly, both neurohormonal pathways seem to be inactive in adult zebrafish hearts. Altogether, our findings support critical roles of two major thermogenic pathways in suppressing heart regenerative capacity, and implicate that the limited regenerative capacity in various adult mammalian tissues may be a tradeoff for the acquisition of endothermy in ontogeny and phylogeny.

On the rules of life and Kleiber's law: the macroscopic relationship between materials and energy

Efforts to accommodate the growth in global energy consumption within a fragile biosphere are primarily focused on managing the transition towards a low-carbon energy mix. We show evidence that a more fundamental problem exists through a scaling relation, akin to Kleiber's Law, between society's energy consumption and material stocks. Humanity's energy consumption scales at 0.78 of its material stocks, which implies predictable environmental pressure regardless of the energy mix. If true, future global energy scenarios imply vast amounts of materials and corresponding environmental degradation, which have not been adequately acknowledged. Thus, limits to energy consumption are needed regardless of the energy mix to stabilize human intervention in the biosphere.

Allometry between Suture Line Length and Phragmocone Volume in Some Cretaceous Ammonoids

The allometric relationship between suture line length and phragmocone volume was examined in 28 specimens belonging to six ammonoid species recovered from the Upper Cretaceous Yezo Group of Hokkaido, Japan. The suture perimeter was calculated by summing the distances between digitized points along the suture line in a photograph. The phragmocone volume was calculated using a modified Raup's model. The relationship between suture perimeter and phragmocone volume in each species was expressed as an allometric equation on a logarithmic scale. The exponent of ontogenetic allometry estimated for each species ranged from 0.462 to 0.626. The exponents estimated were much greater than the exponent in the case of isometry (0.333) and the value previously obtained through interspecific comparison. Calculation using a theoretical morphologic model indicates that allometric exponents for the suture perimeter of approximately 0.5 reflect positive allometry of the septal surface area with respect to body size. The present results suggest that strong positive allometry of the suture perimeter leads to a considerable positive allometry of the septal surface area resulting in satisfying Kleiber's scaling law, although its functional significance remains unclear.

Teaching Body Mass Index and Kleiber Law

Scaling laws advise that resting metabolic rates in animals and their corresponding body surfaces both should follow [Formula: see text] dependence. A pedagogic attempt has been made to validate this Kleiber law in case of human beings having spherical head and cylindrical arms, legs and trunk with the help of associated body mass index. It is observed that the metabolic rates of those persons who either lose or put on weight are not affected provided their body parts are functioning properly. It is suggested that matching body mass indices should also be worked out for animals.

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.

Body size-dependent energy storage causes Kleiber's law scaling of the metabolic rate in planarians.

Kleiber's law, or the 3/4 -power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber's law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body mass over 3 orders of magnitude reveal that Kleiber's law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber's law in planarians and have general implications for understanding a fundamental scaling law in biology.

Allometric scaling of microbial fuel cells and stacks: The lifeform case for scale-up

This case study reports for the first time on the comparison between allometric scaling of lifeforms and scale-up of microbial fuel cell entities; enlarging individual units in volume, footprint and electrode surface area but also multiplying a static size/footprint and electrode surface area to scale-up by stacking. A study published in 2010 by DeLong et al. showed for the first time that Kleiber's law does not apply uniformly to all lifeforms, and that in fact growth rate for prokaryotes is superlinear, for protists is linear and for metazoa is sublinear. The current study, which is utilising data from previous experiments, is showing for the first time that for individual MFC units, which are enlarged, growth rate/power is sublinear, whereas for stacks this is superlinear.

A general model for metabolic scaling in self-similar asymmetric networks.

How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.

Villus packing density and lacunarity: Markers of placental efficiency?

We evaluate, in routine H&E histology slides, villus quantity in a given area (villous packing density, VPD) and the pattern or “gappiness” of villous distribution (lacunarity), and test for correlations with a proxy for fetoplacental metabolic rate, β calculated as (ln (placental weight)/ln (birthweight)) from Kleiber's law [1].Three ∼4.3 mm2 images each were obtained from 88 term placentas. Ranges of VPD and lacunarity were each correlated with β (r = 0.31, p = 0.003, r = 0.23, p = 0.03 and respectively). The relationship between β and within-placenta variation in VPD and lacunarity highlights the need to study not merely the mean but the variance of villous geometries and spatial distributions.

Fossil skulls reveal that blood flow rate to the brain increased faster than brain volume during human evolution.

The evolution of human cognition has been inferred from anthropological discoveries and estimates of brain size from fossil skulls. A more direct measure of cognition would be cerebral metabolic rate, which is proportional to cerebral blood flow rate (perfusion). The hominin cerebrum is supplied almost exclusively by the internal carotid arteries. The sizes of the foramina that transmitted these vessels in life can be measured in hominin fossil skulls and used to calculate cerebral perfusion rate. Perfusion in 11 species of hominin ancestors, from Australopithecus to archaic Homo sapiens, increases disproportionately when scaled against brain volume (the allometric exponent is 1.41). The high exponent indicates an increase in the metabolic intensity of cerebral tissue in later Homo species, rather than remaining constant (1.0) as expected by a linear increase in neuron number, or decreasing according to Kleiber's Law (0.75). During 3 Myr of hominin evolution, cerebral tissue perfusion increased 1.7-fold, which, when multiplied by a 3.5-fold increase in brain size, indicates a 6.0-fold increase in total cerebral blood flow rate. This is probably associated with increased interneuron connectivity, synaptic activity and cognitive function, which all ultimately depend on cerebral metabolic rate.

Kleiber's Law: How the Fire of Life ignited debate, fueled theory, and neglected plants as model organisms

Size is a key feature of any organism since it influences the rate at which resources are consumed and thus affects metabolic rates. In the 1930s, size-dependent relationships were codified as “allometry” and it was shown that most of these could be quantified using the slopes of log-log plots of any 2 variables of interest. During the decades that followed, physiologists explored how animal respiration rates varied as a function of body size across taxa. The expectation was that rates would scale as the 2/3 power of body size as a reflection of the Euclidean relationship between surface area and volume. However, the work of Max Kleiber (1893–1976) and others revealed that animal respiration rates apparently scale more closely as the 3/4 power of body size. This phenomenology, which is called “Kleiber's Law,” has been described for a broad range of organisms, including some algae and plants. It has also been severely criticized on theoretical and empirical grounds. Here, we review the history of the analysis of metabolism, which originated with the works of Antoine L. Lavoisier (1743–1794) and Julius Sachs (1832–1897), and culminated in Kleiber's book The Fire of Life (1961; 2. ed. 1975). We then evaluate some of the criticisms that have been leveled against Kleiber's Law and some examples of the theories that have tried to explain it. We revive the speculation that intracellular exo- and endocytotic processes are resource delivery-systems, analogous to the supercellular systems in multicellular organisms. Finally, we present data that cast doubt on the existence of a single scaling relationship between growth and body size in plants.

Reprint of “Zooplankton biomass and electron transport system activity around the Balearic Islands (western Mediterranean)”

Measuring electron transport system (ETS) activity in zooplankton provides an index of respiration, theoretically, the potential respiration rate. We apply the ETS technique to estimate potential respiration and carbon demand from the zooplankton community in the upper 200m of the water column near the Balearic Islands. The investigation was focused on two areas with different oceanographic conditions: the Balearic and Algerian subbasins. It compared the biomass, potential respiration and specific potential respiration of different size fractions (53–200, 200–500, >500μm) in both areas. In these regions the largest contribution to respiration was found in the larger sizes. The specific respiration (per unit biomass) was greater in smaller fractions, indicating that they have a more active metabolism. Both biomass and potential respiration increased in the Algerian subbasin and for both regions biomass and potential respiration were greater in shallow waters over the continental shelf (<200m). Using Kleiber's law as a tool to investigate the relationships between these two variables, we found that the exponential relation coefficient (b) was less than 0.75, indicating that the respiration was depressed (shifted down). In cultures and in eutrophic ocean waters (upwelling areas) b normally is greater than 0.75, consequently we intuit that the low value of b over the Balearic and Algerian subbasins indicates that the zooplankton is not well fed and that they are living under oligotrophic stress.

Calcium handling in muscle fibres of mice and men: evolutionary adaptation in different species to optimize performance and save energy

Calcium handling in muscle fibres of mice and men: evolutionary adaptation in different species to optimize performance and save energy

Zooplankton biomass and electron transport system activity around the Balearic Islands (western Mediterranean)

Measuring electron transport system (ETS) activity in zooplankton provides an index of respiration, theoretically, the potential respiration rate. We apply the ETS technique to estimate potential respiration and carbon demand from the zooplankton community in the upper 200m of the water column near the Balearic Islands. The investigation was focused on two areas with different oceanographic conditions: the Balearic and Algerian subbasins. It compared the biomass, potential respiration and specific potential respiration of different size fractions (53–200, 200–500, >500μm) in both areas. In these regions the largest contribution to respiration was found in the larger sizes. The specific respiration (per unit biomass) was greater in smaller fractions, indicating that they have a more active metabolism. Both biomass and potential respiration increased in the Algerian subbasin and for both regions biomass and potential respiration were greater in shallow waters over the continental shelf (<200m). Using Kleiber's law as a tool to investigate the relationships between these two variables, we found that the exponential relation coefficient (b) was less than 0.75, indicating that the respiration was depressed (shifted down). In cultures and in eutrophic ocean waters (upwelling areas) b normally is greater than 0.75, consequently we intuit that the low value of b over the Balearic and Algerian subbasins indicates that the zooplankton is not well fed and that they are living under oligotrophic stress.

Oxygen Consumption Rates of Bacteria under Nutrient-Limited Conditions

Many environments on Earth experience nutrient limitation and as a result have nongrowing or very slowly growing bacterial populations. To better understand bacterial respiration under environmentally relevant conditions, the effect of nutrient limitation on respiration rates of heterotrophic bacteria was measured. The oxygen consumption and population density of batch cultures of Escherichia coli K-12, Shewanella oneidensis MR-1, and Marinobacter aquaeolei VT8 were tracked for up to 200 days. The oxygen consumption per CFU (QO2) declined by more than 2 orders of magnitude for all three strains as they transitioned from nutrient-abundant log-phase growth to the nutrient-limited early stationary phase. The large reduction in QO2 from growth to stationary phase suggests that nutrient availability is an important factor in considering environmental respiration rates. Following the death phase, during the long-term stationary phase (LTSP), QO2 values of the surviving population increased with time and more cells were respiring than formed colonies. Within the respiring population, a subpopulation of highly respiring cells increased in abundance with time. Apparently, as cells enter LTSP, there is a viable but not culturable population whose bulk community and per cell respiration rates are dynamic. This result has a bearing on how minimal energy requirements are met, especially in nutrient-limited environments. The minimal QO2 rates support the extension of Kleiber's law to the mass of a bacterium (100-fg range).

Kleiber′s law and the A 1 chieve study

Kleiber's law is a near-universal maxim of biology. Being one of the allometric scaling laws, this 3/4 power law for metabolic rates is characteristic of all organisms, and states that as the size of a living organism grows, its life span increases, and heart beat reduces by three-fourth square. Simply put, it means that an elephant, which is x times larger than a mouse, has an x¾ heart rate as compared to its murine friend. Identified by Kleiber in the 1930s, while working on comparative animal physiology, this law has since been found to hold true in a wide variety of situations, including plants and bacteria.[1] An even more surprising finding, however, has been the discovery of situations where Kleiber's law holds true in inverse. When studying urban environments, Bettencourt et al. realized that human social organizations are extensions of biology, following similar principles and constraints as well. Cities obey this law as well, but sometimes with a positive rather than negative scaling correlation. As group of people grow in number, its original or creative or scientific output expands, not linearly, but exponentially, as its 5/4th power. To paraphrase in simple words, if n scientists produce x publications, 2n researchers will produce, not 2n, but 2n5/4 papers. This superlinear scaling is applicable to almost all sociological organization, including creation of patents and inventions.[2] Though the versatility of this seemingly elementary law has been criticized, this observation is important from a diabetology and endocrinology perspective. The world is experiencing an unprecedented pandemic of lifestyle diseases with diabetes being the most visible face. This surge in incidenceand prevalence of diabetes is matched by an increase in the number of scientific publications related to this condition. A search on PubMed or Google scholar reveals a virtual explosion in the number and size of clinical trials in diabetes. However, none of these trials compares in magnitude with the A1chieve trial. The A1chieve study has set new landmarks in clinical research in terms of number of continents, countries, clinical sites, subjects and insulins that have been studied.[3] The enormity of this observational trial is reflected in the data that has been published related to this study. Prestigious international journals such as Diabetes Research and Clinical Practice (DRCP) and premier opinion-building Indian publications like Journal of Association of Physicians of India (JAPI) have devoted special issues to A1chieve. As Dr. Siddharth Shah, editor JAPI, clarifies: “We have responsibility to publish, with an obligation towards the participants and the investigators.”[4] But back to the Kleiber's Law. The cross-country, multi-insulin nature of this trial and the wide spectrum of data collected over an appreciably long time contribute to the robust nature of A1chieve results. Put together, all this data should result in superlinear scaling of energy rather synergy amongst all stakeholders. This issue of Indian J Endocrinology Metabolism should foster an understanding of our short comings and an appreciation of the effective, safe and well-tolerated insulin analogues available to us. More importantly, it should act as a stimulus for bench marking and experience sharing among different clinical practices, regions and countries. In this manner, the A1chieve study and the Indian Journal of Endocrinology and Metabolism should lay the ground for a superlinear improvement in the quality of diabetes care throughout the world.

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&gt;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.