scholarly journals The Principle of Similitude in Biology: From Allometry to the Formulation of Dimensionally Homogenous ‘Laws’

2018 ◽  
Author(s):  
Andrés Escala
Keyword(s):  
Body Mass ◽  
Basal Metabolic Rate ◽  
Homogeneous Equation ◽  
Laws Of Nature ◽  
Life Sciences ◽  
Metabolic Rates ◽  
Basic Requirement ◽  
Ecological Implications ◽  
New Formulation ◽  
Dimensional Homogeneity

ABSTRACTMeaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the Π theorem (Vaschy 1892; Buckingham 1914). However, most relations in allometry do not satisfy this basic requirement, including the ‘3/4 Law’ (Kleiber 1932) that relates the basal metabolic rate and body mass, besides it is sometimes claimed to be the most fundamental biological rate (Brown et al. 2004) and the closest to a law in life sciences (Brown et al. 2004). Using the Π theorem, here we show that it is possible to construct an unique homogeneous equation for the metabolic rates, in agreement with data in the literature. We find that the variations in the dependence of the metabolic rates on body mass are secondary, coming from variations in the allometric dependence of the heart frequencies. This includes not only different classes of animals (mammals, birds, invertebrates) but also different aerobic conditions (basal and maximal). Our results demonstrate that most of the differences found in the allometric exponents (White et al. 2007) are due to compare incommensurable quantities and that our dimensionally homogenous formula, unify these differences into a single formulation. We discuss the ecological implications of this new formulation in the context of the Malthusian’s, Fenchel’s and Calder’s relations.

Do season and distribution affect thermal energetics of a hibernating bat endemic to the tropics and subtropics?

2011 ◽  
Vol 301 (2) ◽  
pp. R542-R547 ◽  
Author(s):  
Clare Stawski ◽  
Fritz Geiser
Keyword(s):  
Body Temperature ◽  
Body Mass ◽  
Basal Metabolic Rate ◽  
Seasonal Changes ◽  
Metabolic Rates ◽  
Open Flow ◽  
Thermoneutral Zone ◽  
In The Wild ◽  
Thermal Energetics ◽  
The Tropics

Although many tropical and subtropical areas experience pronounced seasonal changes in weather and food availability, few studies have examined and none have compared the thermal physiology and energetics of a hibernating mammal that is restricted to these regions. We quantified thermal energetics of northern long-eared bats ( Nyctophilus bifax; body mass ∼10 g) during summer, winter, and spring from a subtropical habitat, and also during winter from a tropical habitat, to determine how N. bifax cope with climate and seasonal changes in weather. We captured bats in the wild and measured metabolic rates via open-flow respirometry. The basal metabolic rate of subtropical bats at an ambient temperature (Ta) of 32.6 ± 0.7°C was 1.28 ± 0.06 ml O2·g−1·h−1 during both summer and winter, similar to other species of Nyctophilus. Resting metabolic rates below the thermoneutral zone increased similarly with decreasing Ta during all seasons and in both regions. All individuals showed a high proclivity to enter torpor at Ta values below the thermoneutral zone. Metabolic rates in torpid thermoconforming bats fell with Ta and body temperature, and mean minimum metabolic rates during torpor were similar during all seasons and in both regions and as predicted from body mass in temperate zone hibernators. At very low Ta, torpid N. bifax thermoregulated, and this threshold Ta differed significantly between subtropical (Ta = 3.5 ± 0.3°C) and tropical (Ta = 6.7 ± 0.7°C) individuals, but not between seasons. Our data show that thermal energetics of N. bifax do not vary seasonally and in many aspects are similar in tropical and subtropical bats; however, torpid individuals from the subtropics allow body temperature to fall to significantly lower values than those from the tropics.

The relationship between body mass and rate of rewarming from hibernation and daily torpor in mammals

1990 ◽  
Vol 151 (1) ◽  
pp. 349-359 ◽  
Author(s):  
F. Geiser ◽  
R. V. Baudinette
Keyword(s):  
Metabolic Rate ◽  
Body Mass ◽  
Air Temperature ◽  
Basal Metabolic Rate ◽  
Strong Relationship ◽  
The Other ◽  
Daily Torpor ◽  
Pronounced Increase ◽  
The Relationship

1. Rewarming rate from torpor and body mass were inversely related in 86 mammals ranging in body mass between 2 and 8500 g. 2. Most of the mammalian taxa investigated showed a similar change of rewarming rate with body mass. Only the insectivores showed a more pronounced increase in rewarming with a decrease in body mass than did the other taxa. The rates of rewarming of marsupials were similar to those of placentals. 3. At low air temperature (Ta), the rate of rewarming of marsupials was not related to body mass, although a strong relationship between the two variables was observed in the same species at high Ta. 4. The slopes relating rewarming rates and body mass of the mammalian groups and taxa analysed here were similar to those obtained earlier for mass-specific basal metabolic rate (BMR) and body mass in mammals, suggesting that the rate of rewarming and BMR are physiologically linked.

scholarly journals Allometry of mitochondrial efficiency is set by metabolic intensity

2019 ◽  
Vol 286 (1911) ◽  
pp. 20191693 ◽  
Author(s):  
Boël Mélanie ◽  
Romestaing Caroline ◽  
Voituron Yann ◽  
Roussel Damien
Keyword(s):  
Metabolic Rate ◽  
Body Mass ◽  
Coupling Efficiency ◽  
Energy Output ◽  
Scaling Exponent ◽  
Metabolic Rates ◽  
Mammal Species ◽  
Skeletal Muscle Mitochondria ◽  
Metabolic Intensity ◽  
Mitochondrial Efficiency

Metabolic activity sets the rates of individual resource uptake from the environment and resource allocations. For this reason, the relationship with body size has been heavily documented from ecosystems to cells. Until now, most of the studies used the fluxes of oxygen as a proxy of energy output without knowledge of the efficiency of biological systems to convert oxygen into ATP. The aim of this study was to examine the allometry of coupling efficiency (ATP/O) of skeletal muscle mitochondria isolated from 12 mammal species ranging from 6 g to 550 kg. Mitochondrial efficiencies were measured at different steady states of phosphorylation. The efficiencies increased sharply at higher metabolic rates. We have shown that body mass dependence of mitochondrial efficiency depends on metabolic intensity in skeletal muscles of mammals. Mitochondrial efficiency positively depends on body mass when mitochondria are close to the basal metabolic rate; however, the efficiency is independent of body mass at the maximum metabolic rate. As a result, it follows that large mammals exhibit a faster dynamic increase in ATP/O than small species when mitochondria shift from basal to maximal activities. Finally, the invariant value of maximal coupling efficiency across mammal species could partly explain why scaling exponent values are very close to 1 at maximal metabolic rates.

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

2007 ◽  
Vol 292 (6) ◽  
pp. R2115-R2121 ◽  
Author(s):  
Melanie F. Brown ◽  
Tyson P. Gratton ◽  
Jeffrey. A. Stuart
Keyword(s):  
Metabolic Rate ◽  
Body Mass ◽  
Oxygen Delivery ◽  
Mammalian Cells ◽  
Cultured Cells ◽  
Mammalian Species ◽  
Cellular Respiration ◽  
Metabolic Rates ◽  
Respiration Rates ◽  
Species Specific

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.

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