Organ-Tissue Level Model of Resting Energy Expenditure Across Mammals: New Insights into Kleiber's Law

Abstract

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo>=</mml:mo><mml:mn>70.0</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>0.75</mml:mn></mml:mrow></mml:msup></mml:math>. 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. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> predicted by the organ-tissue level model was correlated with body mass (correlation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>0.9975</mml:mn></mml:math>) and resulted in the function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">66.33</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">0.754</mml:mn></mml:mrow></mml:msup></mml:math>, with a coefficient and scaling exponent, respectively, close to 70.0 and 0.75 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi>P</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.05</mml:mn></mml:math>) as observed by Kleiber. There were no differences between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> calculated by Kleiber’s law; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> was correlated (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>0.9994</mml:mn></mml:math>) with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>. The mass-specific <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:mrow><mml:msub><mml:mrow><mml:mtext>REE</mml:mtext></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>, that is, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mrow><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mtext>REE</mml:mtext><mml:mo>/</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>, was correlated with body mass (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M13"><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>0.9779</mml:mn></mml:math>) 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.