Why base metabolism varies with mass

An adult human in absolute rest and at a 20º C room temperature consumes approximately one calorie per kilo and hour. However, an elephant burns half a calorie per kilo of mass in the same amount of time, while a mouse burns an astonishing 70 calories per kilo. What causes this difference?

One of the first people to realise this occurrence was German physiologist Max Rubner while studying the base metabolism of different size dogs in 1883. Rubner suggested that what caused the phenomenon was the heat that was lost through the skin. The surface of the skin varies according to the size of the animal squared, whereas its volume varies by the size cubed, which would imply that base metabolism B varies proportionately to the mass raised to the power of 2/3, M2/3. However, in 1932, measurements that Swiss biologist Max Kleiber performed for mammals of a larger range of masses, including oxen and rats, seemed to indicate that changes in metabolism followed M3/4, a figure we now know as Kleiber's law.

The search for an explanation to this figure ignited an intense debate for decades which seemingly came to an end in 1997 with the fractal model of physicist Geoffrey West et al. This model explained the exponent with the fractal form of the organism's networks of resource distribution, such as the circulatory or respiratory systems. Measuring an organism's base figure is a delicate and laborious task. As the number of metabolic measurements increased by performing measurements on more animals, the fractal model started to show more and more inconsistencies, to the point that in some groups of animals such as small birds or insects, the 3/4 exponent does not fit. Even for mammals, for which Kleiber's law was conceived, data shows noticeable divergence compared to the theory behind the law.

Now the authors of an article recently published in Scientific Reports, Fernando J. Ballesteros and Vicent J. Martínez (Astronomic Observatory of the Universitat de València-Parc Científic), Bartolo Luque (Aeronautic engineer at the E.T.S.I. of the Universidad Politécnica de Madrid), Lucas Lacasa (School of Mathematical Sciences, Queen Mary University of London), Enric Valor (Thermodynamic department of the Universitat de València) and Andrés Moya (Integrative and Systems Biology-UV/CSIC, in the Parc Científic), have found the piece that completes the puzzle from an Astrophysics theoretic model. "While we were writing the 'Fractales y caos' book, where we talk about Kleyber's law, we realized that the fractal model of West and co. didn't fit. The thermal explanation seemed more natural, but the energetic part that doesn't dissipate like heat, had to be taken into account," explains Fernando Ballesteros. "Vicent and I added this to the thermal method and we saw that the data fit perfectly with our theory. Andrés immediately realized that out model was a trade off, an evolutionary exchange, and we perfected it together. Enric gave the thermal method solidity after the trade off, and Bartolo and Lucas expanded the work to living beings other than mammals, confirming its predictive power," he concludes.

Scientists propose this solution as a compromise between passive caloric dissipation and cellular maintenance's minimum energy consumption. Not all energy that an organism consumes is transformed into heat; one part is used for cell division, another to synthesize proteins… in other words, to support the organism and allow it to work. If all energy was transformed into heat, consumption would in fact be equal to a 2/3 power, but then we would be referring to a heater rather than an organism. On the other hand, if all energy was consumed efficiently, consumption would be directly proportional to the number of cells, that is to say, mass M -- but part of it is inevitably lost as heat. Real organisms balance both extremes. The weighted sum of both components, one proportional to mass M and another to M2/3 -- in other words, B = aM + bM2/3 -- explains the curve in mammal's base metabolism and the different relations found amongst different animal groups, but also the metabolic differences between desert and polar animals, or even for plant metabolism.