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 . 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. predicted by the organ-tissue level model was correlated with body mass (correlation ) and resulted in the function , with a coefficient and scaling exponent, respectively, close to 70.0 and 0.75 ( ) as observed by Kleiber. There were no differences between and calculated by Kleiber’s law; was correlated ( ) with . The mass-specific , that is, , was correlated with body mass ( ) 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. 1. Introduction Resting energy expenditure (REE), defined as the whole-body energy expenditure under standard conditions, is the largest fraction of total energy expenditure. Body mass was applied early in exploring the quantitative association between REE and body composition. The best empirical fit between REE (in kcal/d) and body mass (M, in kg) from mouse to elephant with a ~330,000-fold difference in body size was derived by Kleiber [1, 2] and Brody [3], Equation (1) is the well-known Kleiber’s law or power law, one of the most widely discussed rules in bioenergetics [2, 4]. Based on (1), Kleiber’s law can also be expressed in terms of mass-specific REE, According to Kleiber’s law, small mammals (e.g., shrew) have lower REE but higher REE/M than do large mammals (e.g., elephant). Although many investigators have attempted to clarify plausible mechanisms, a full understanding of Kleiber’s law is still uncertain and represents a knowledge gap in the studies of bioenergetics [12]. Primary
References
[1]
M. Kleiber, “Body size and metabolism,” Hilgardia, vol. 6, pp. 315–353, 1932.
[2]
M. Kleiber, The Fire of Life. An Introduction to Animal Energetics, Wiley, New York, NY, USA, 1961.
[3]
S. Brody, Bioenergetics and Growth, with Special Reference to the Efficiency Complex in Domestic Animals, Reinhold, New York, NY, USA, 1945.
[4]
C. W. Hall, Laws and Models: Science, Engineering, and Technology, CRC Press, New York, NY, USA, 1999.
[5]
J. A. Greenberg, “Organ metabolic rates and aging: two hypotheses,” Medical Hypotheses, vol. 52, no. 1, pp. 15–22, 1999.
[6]
R. W. Brauer, “Liver circulation and function,” Physiological Reviews, vol. 43, pp. 178–213, 1963.
[7]
M. Elia, “Organ and tissue contribution to metabolic rate,” in Energy Metabolism: Tissue Determinants and Cellular Corollaries, J. M. Kinney and H. N. Tucker, Eds., pp. 19–60, Raven Press, New York, NY, USA, 1992.
[8]
K. Schmidt-Nielsen, Scaling: Why Is Animal Size so Important?Cambridge University Press, Cambridge, UK, 1984.
[9]
A. W. Martin and F. A. Fuhrman, “The relationship between summated tissue respiration and metabolic rate in the mouse and dog,” Physiological Zoology, vol. 28, pp. 18–34, 1955.
[10]
W. S. Snyder, M. J. Cook, E. S. Nasset, L. R. Karhausen, G. P. Howells, and I. H. Tipton, Report of the Task Group on Reference Man, Pergamon Press, Oxford, UK, 1975.
[11]
A. Navarrete, P. Carel, C. P. van Schaik, and K. Isler, “Energetics and the evolution of human brain size. Supplementary Information,” Nature, vol. 480, pp. 91–94, 2011.
[12]
P. S. Agutter and D. N. Wheatley, “Metabolic scaling: consensus or controversy?” Theoretical Biology and Medical Modelling, vol. 1, pp. 13–24, 2004.
[13]
D. Gallagher, D. Belmonte, P. Deurenberg et al., “Organ-tissue mass measurement allows modeling of REE and metabolically active tissue mass,” American Journal of Physiology, vol. 275, no. 2, pp. E249–E258, 1998.
[14]
Z. Wang, S. Heshka, S. B. Heymsfield, W. Shen, and D. Gallagher, “A cellular-level approach to predicting resting energy expenditure across the adult years,” American Journal of Clinical Nutrition, vol. 81, no. 4, pp. 799–806, 2005.
[15]
W. A. Calder III, Size, Function, and Life History Publications, Dover, New York, NY, USA, 1984.
[16]
P. Couture and A. J. Hulbert, “Relationship between body mass, tissue metabolic rate, and sodium pump activity in mammalian liver and kidney,” American Journal of Physiology, vol. 268, no. 3, pp. R641–R650, 1995.
[17]
Z. Wang, T. P. O'Connor, S. Heshka, and S. B. Heymsfield, “The reconstruction of Kleiber's law at the organ-tissue level,” Journal of Nutrition, vol. 131, no. 11, pp. 2967–2970, 2001.
[18]
Z. M. Wang, “High ratio of resting energy expenditure to body mass in childhood and adolescence: a mechanistic model,” American Journal of Human Biology, vol. 24, pp. 460–467, 2012.
[19]
T. A. McMahon, “Using body size to understand the structural design of animals: quadrupedal locomotion,” Journal of Applied Physiology, vol. 39, no. 4, pp. 619–627, 1975.
[20]
J. J. Blum, “On the geometry of four-dimensions and the relationship between metabolism and body mass,” Journal of Theoretical Biology, vol. 64, no. 3, pp. 599–601, 1977.
[21]
A. C. Economos, “Gravity, metabolic rate and body size of mammals,” Physiologist, vol. 22, no. 6, pp. S71–72, 1979.
[22]
M. R. Patterson, “A mass transfer explanation of metabolic scaling relations in some aquatic invertebrates and algae,” Science, vol. 255, no. 5050, pp. 1421–1423, 1992.
[23]
G. B. West, J. H. Brown, and B. J. Enquist, “The fourth dimension of life: fractal geometry and allometric scaling of organisms,” Science, vol. 284, no. 5420, pp. 1677–1679, 1999.
[24]
J. R. Banavar, A. Maritan, and A. Rinaldo, “Size and form in efficient transportation networks,” Nature, vol. 399, no. 6732, pp. 130–132, 1999.
[25]
C. A. Darveau, R. K. Suarez, R. D. Andrews, and P. W. Hochachka, “Allometric cascade as a unifying principle of body mass effects on metabolism,” Nature, vol. 417, no. 6885, pp. 166–170, 2002.
[26]
Z. M. Wang, R. N. Pierson, and S. B. Heymsfield, “The five-level model: a new approach to organizing body-composition research,” American Journal of Clinical Nutrition, vol. 56, no. 1, pp. 19–28, 1992.
[27]
Z. Wang, S. Heshka, K. Zhang, C. N. Boozer, and S. B. Heymsfield, “Resting energy expenditure: systematic organization and critique of prediction methods,” Obesity Research, vol. 9, no. 5, pp. 331–336, 2001.
[28]
B. Linde, P. Hjemdahl, U. Freyschuss, and A. Juhlin-Dannfelt, “Adipose tissue and skeletal muscle blood flow during mental stress,” American Journal of Physiology, vol. 256, no. 1, pp. E12–E18, 1989.
[29]
K. K. McCully and J. D. Posner, “The application of blood flow measurements to the study of aging muscle,” Journals of Gerontology, vol. 50, pp. 130–136, 1995.
[30]
H. T. Chugani, “Metabolic imaging: a window on brain development and plasticity,” Neuroscientist, vol. 5, no. 1, pp. 29–40, 1999.