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First published online April 26, 2005
Journal of Experimental Biology 208, 1709-1716 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01421

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Review article: Circulation and body size

Control of metabolic rate is a hidden variable in the allometric scaling of homeotherms

José Guilherme Chaui-Berlinck^1,*, Carlos Arturo Navas¹, Luiz Henrique Alves Monteiro² and José Eduardo Pereira Wilken Bicudo¹

¹ Departamento de Fisiologia, Instituto de Biociências, Universidade de São Paulo, Rua do Matão tr. 14, 321, CEP: 05508-900, São Paulo/SP, Brazil
² Departamento de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo and Pós-Graduação, Engenharia Elétrica, Universidade Presbiteriana Mackenzie, Rua da Consolação 896, CEP:01302-907, São Paulo/SP, Brazil

^* Author for correspondence (e-mail: jgcb{at}usp.br)

Accepted 30 November 2005

Summary

The allometric scaling exponent of the relationship between standard metabolic rate (SMR) and body mass for homeotherms has a long history and has been subject to much debate. Provided the external and internal conditions required to measure SMR are met, it is tacitly assumed that the metabolic rate (B) converges to SMR. If SMR does indeed represent a local minimum, then short-term regulatory control mechanisms should not operate to sustain it. This is a hidden assumption in many published articles aiming to explain the scaling exponent in terms of physical and morphological constraints. This paper discusses the findings of a minimalist body temperature (T_b) control model in which short-term controlling operations, related to the difference between T_b and the set-point temperatures by specific gains and time delays in the control loops, are described by a system of differential equations of T_b, B and thermal conductance. We found that because the gains in the control loops tend to increase as body size decreases (i.e. changes in B and thermal conductance are speeded-up in small homeotherms), the equilibrium point of the system potentially changes from asymptotically stable to a centre, transforming B and T_b in oscillating variables. Under these specific circumstances the very concept of SMR no longer makes sense. A series of empirical reports of metabolic rate in very small homeotherms supports this theoretical prediction, because in these animals B seems not to converge to a SMR value. We conclude that the unrestricted use of allometric equations to relate metabolic rate to body size might be misleading because metabolic control itself experiences size effects that are overlooked in ordinary allometric analysis.

Key words: control, body temperature, metabolic rate, allometry, dynamic system

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