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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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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

View larger version (49K): [in a new window]   Fig. 1. Standard metabolic rate concept. There are internal and external conditions that once met supposedly lead the metabolic rate B of a homeotherm to the SMR. This is, thus, a local minimum of B (B=0). See text for further discussion.

View larger version (25K): [in a new window]   Fig. 2. (A) Biological basis of Tb control. am, metabolic proportionality factor; endoc. law, endocrine controllers law; shiv, shivering thermogenesis; non-shiv, non-shivering thermogenesis. These four blocks constitute the metabolic rate controller/process in our model (see B). Behav. law, posture controllers law; aK, proportionality factor for non-evaporative heat transfer; aEHL, proportionality factor for evaporative heat transfer; shape, body positioning; vasomotor: peripheral blood perfusion; S/P, sweating and panting. These six blocks constitute the thermal conductance controller/process in our model (see B). HP, heat production; HL, heat loss; TC/S, core and skin temperatures. The thermal characteristics of the body correspond to the thermal inertia and `disturbances' to TA in our model. Notice that our model does not take into account local loops and other central nervous system areas interfering in the control. (Scheme based on fig. 2 of Cooper, 2002). (B) Schematic representation of the Tb control system modelled in Eq. 1-3. See text for details. Compare this control system to the biological one presented in A.

View larger version (17K): [in a new window]   Fig. 3. Exponential (exp; broken lines) and pure polynomial (poly; solid lines) parts of Eq. 5 plotted separately as functions of . The crossing points between the functions are the solutions to the characteristic polynomial of the system. values are shown in the negative real axis portion, thus, crossing points correspond to pure real negative and, therefore, asymptotically stable nodes in the corresponding eigenvector. Notice that at =0, the polynomial part is zero and the exponential part is negative (-bk5). (A) A putative large homeotherm (>1000 g) is represented. Notice the existence of three crossing points. (B) Small (100 g) homeotherm. (C) 50 g homeotherm, represents a putative limiting condition. The functions touch each other just twice. Any further decrease in body mass would make the functions fall apart and two eigenvalues would have imaginary parts, rendering the system a focus. The focus is asymptotically stable while the real part of each complex conjugate belongs to the negative real axis. The focus would become unstable when the complex conjugate has positive real part. This potentially occurs when the functions are `far away' from each other, as depicted in (D), representing a 10 g homeotherm.

View larger version (20K): [in a new window]   Fig. 4. Temporal profiles of Tb and B in conditions representing a large homeotherm (A), a homeotherm weighing a little less than 50 g (B) and a 10 g homeotherm (C). Time in arbitrary units. Solid lines, Tb; broken lines, B. Notice the asymptotically stable node in the large homeotherm condition, the asymptotically stable focus (damped oscillations) in the 50 g condition, and the centre (sustained oscillations) in the 10 g condition. Simulations were done in MatLab 6.1 and Simulink.