The trouble with mass: Multivariate metabolism

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  • Published: Feb 15, 2018
  • Author: David Bradley
  • Channels: Chemometrics & Informatics
thumbnail image: The trouble with mass: Multivariate metabolism


A new analytical approach to the data by a team from Spain and the UK might have solved the riddle of why the bigger an animal is the lower its basal metabolic rate, the minimum energy used to stay alive. Cat photo by David Bradley

A new analytical approach to the data by a team from Spain and the UK might have solved the riddle of why the bigger an animal is the lower its basal metabolic rate, the minimum energy used to stay alive.

A mammal's metabolic rate varies according to body mass so that an elephant might burn half a "calorie" per kilogram of body mass in an hour, a mouse will burn a huge 70 calories, a person might use one calorie per kilo per hour. Why this should be has remained a game of intellectual cat and mouse for more than a century.

German physiologist Max Rubner studied dogs of different size in 1883 and suggested that what underlies the phenomenon is heat loss through the skin. The surface area of an animal's skin varies according to the size of the animal squared, whereas its volume varies by the size cubed. This would imply that the basal metabolic rate, B, varies in proportion with mass raised to the power of 2/3, M2/3. However, in 1932, Swiss biologist Max Kleiber performed measurements with mammals of lots of different types and sizes and found that the variation in metabolic rate follows an M3/4 rule, which we now know as Kleiber's law. This finding suggests that skin surface area does not underpin basal metabolic rate variation across species.

Predictive power

A multidisciplinary team of researchers of the Universitat de València, the Universidad Politécnica de Madrid, and Queen Mary University of London believe they have managed to solve the puzzle. The team publishes details in the journal Scientific Reports.

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.

Valencia's Fernando Ballesteros, Vicent Martínez, Enric Valor, and Andrés Moya, Madrid's Bartolo Luque, and QMU's Lucas Lacasa have found a piece to complete the puzzle from an Astrophysics theoretical model.

"While we were writing our 'Fractales y caos' book, where we talk about Kleyber's law, we realized that the fractal model of West and co. didn't fit," explains Ballesteros. "The thermal explanation seemed more natural, but the energetic part that doesn’t dissipate like heat, had to be taken into account." He adds that he and Martínez "added this to the thermal method and we saw that the data fit perfectly with our theory." Moya recognized immediately that the model was a trade off, an evolutionary exchange, and the team then perfected the details. Valor validated the thermal method, while Luque and Lacasa expanded the model to include animals other than mammals, which confirmed its predictive power.

Model revelations

The researchers suggest that their model reveals a compromise between passive caloric dissipation and the minimum energy consumption for cellular maintenance. Not all energy that an organism consumes is transformed into heat. Some of its energy is used in cell division, some to make proteins and other compounds. All of these processes support the organism and allow it to live. If all of its energy were simply transformed into heat, then consumption would equate to Rubner's M2/3 rule. However, such a rule while applying to a heating appliance would not apply to a living organism. Conversely, if all of the organism's energy were consumed efficiently for metabolic processes other than heat generation, then the consumption rate would be directly proportional to the number of cells comprising the organism.

In the living world, there are all of these other processes and there are inherent inefficiencies as well as heating taking place. Animals, whether alpaca or cat, elephant or mouse, balance the extremes, so that the weighted sum of both components, one proportional to mass M and another to M2/3, gives us a more realistic model of metabolic rate. B = aM + bM2/3. This model also helps explains the different relationship between size and metabolic rate in animals that live in different temperature extremes in tropical deserts or the polar regions, for example. I t might even be extended to plant metabolism, the team hints.

Related Links

Sci Rep 2018, online: "On the thermodynamic origin of metabolic scaling"

Article by David Bradley

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

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