Analytic theories of allometric scaling

Agutter, Paul S.; Tuszyński, Jack A.

doi:10.1242/jeb.054502

Cited by 72 publications

(65 citation statements)

References 107 publications

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“…46,47 Future research will either confirm or reject these propositions, but it is clear that many more detailed measurements of metabolic rates are required and that current theoretical attempts to explain mechanistically why metabolic rates change with increasing body size are inadequate. [48][49][50][51][52][53] Finally, we want to stress that the exact regulatory mechanisms of O 2 -dependent Figure 8. Summary of organ-and cell respiration with reference to the production/release of Adenosine-3-Phosphate (ATP) by mitochondria.…”

Section: Discussionmentioning

confidence: 99%

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Niklas¹,

Kutschera

2015

Plant Signaling & Behavior

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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 (1893Kleiber ( -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.

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Section: Discussionmentioning

confidence: 99%

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Niklas¹,

Kutschera

2015

Plant Signaling & Behavior

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“…Widely accepted exponents for these powers are 0.75 for BMR and 0.87 for exercise-induced MMR (Weibel & Hoppeler, 2005). Various explanations have been given for the numerical values of the power exponents, with none at present being considered entirely satisfactory in the applicability of their basic assumptions or the logical consistency of their mathematical derivations (Weibel & Hoppeler, 2005;Agutter & Tuszynski, 2011;Roux, 2016). In addition, recent analyses established the validity of a range of numerical values for the BMR and MMR power exponents with 0.75 or 0.87 mostly indicated as central, average, or commonly occurring values (Glazier, 2005).…”

Section: Introductionmentioning

confidence: 99%

Basal metabolic rate scaled to body mass between species by the fractal dimension of the vascular system and body composition

Roux¹

2017

SA J. An. Sci.

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Exercise-induced maximum aerobic metabolic rate (MMR) is related to the fractal dimension (D) of the self-similar vascular blood transport system by a whole body mass (M w ) power with exponent b of the form b = D/3. The principle of self-similarity of the vascular system is in agreement with each organ in the body having a major artery supplying it with blood from the heart and a major vein returning it. This implies that the whole body fractal vascular dimension D is also applicable to all organs or collections of organs such as the viscera and skeletal muscle. The principal reason that basal metabolic rate (BMR) and MMR scale with different power exponents to whole body mass is that MMR is due mainly to respiration in skeletal muscle during exercise and BMR to respiration in the viscera during rest. It follows, therefore, from the self-similarity of the vascular system that BMR is related to viscera mass (M v Here this approach is justified by an assessment of the scaling of viscera and its components with total body mass. The applicability of fractal vascular scaling to the sum of visceral organ metabolic rate contributions is confirmed from organ tissue slices, mitochondrial surface areas, and blood oxygen transport. Estimates obtained from oxygen halfsaturation partial pressure scaling exponents show that BMR scaling with b 2 is of general occurrence between species.

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“…Regularity in the scaling of metabolic rates with body mass is of fundamental importance in biology (Agutter & Tuszynski, 2011). This scaling regularity proved to be difficult to explain, so that the effort by West et al (1997;1999), based on surface and distribution network fractals, was initially well received.…”

Section: Introductionmentioning

confidence: 99%

“…This scaling regularity proved to be difficult to explain, so that the effort by West et al (1997;1999), based on surface and distribution network fractals, was initially well received. Nonetheless, recently their approach has attracted a wide range of methodological, mathematical and empirical criticisms, not all of which have been answered satisfactorily (Agutter & Tuszynski, 2011). For surface area scaling with body mass (M), Pennycuick (1992) and Weibel & Hoppeler (2005) hypothesized an alternative fractal surface solution in terms of a body mass power ( ) characterized by an exponent , with denoting the fractal dimension of the surface involved in metabolic control.…”

Section: Introductionmentioning

confidence: 99%

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Exercise-induced maximum metabolic rate scaled to body mass by the fractal dimension of the vascular distribution network

Roux¹

2016

SA J. An. Sci.

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The central postulation of the present approach to metabolic rate scaling is that exercise-induced maximum aerobic metabolic rate (MMR) is proportional to the fractal extent ( ) of an animal. Total fractal extent can be calculated from the sum of the fractal extents of the capillary service units, as specified by the formula , where means "proportional to". Here is the number of capillaries and is capillary length, with the fractal dimension of the vascular distribution network and with the fractal extent of a capillary service unit. can be any real number in the interval . From dimensional considerations scales with body mass (M) with power exponent , or . Then with follows from the postulate . The utility of the relationship depends on the feasibility of estimating . There are two possibilities. The first is to estimate D from the scaling of aorta cross-section area with body mass. The second is from morphometric observations on various body organs. Both give estimates of in remarkable agreement with estimates obtained by exercise induction or oxygen half-saturation pressure scaling with body mass. The predicted range is experimentally observed. Likely causes of notable particular instances of the symmorphosis with include optimal movement requirements, muscle stress limitation, and maximized oxygen delivery and metabolic rates. Lastly, it is shown that the scaling exponent of basal metabolic rate with body mass can be obtained by taking body composition into account in the product of the scaling exponents of MMR and visceral mass. ______________________________________________________________________________________ Key words: basal metabolic rate, fractal dimension, fractal extent, maximum metabolic rate, vascular distribution network # Corresponding

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Analytic theories of allometric scaling

Cited by 72 publications

References 107 publications

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Basal metabolic rate scaled to body mass between species by the fractal dimension of the vascular system and body composition

Exercise-induced maximum metabolic rate scaled to body mass by the fractal dimension of the vascular distribution network

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