Metabolic scaling is one of the central enigmas of comparative biology. Oxygen consumption, as a proxy for aerobic metabolism, does not scale proportionally with body mass. Expressed as an exponential function, oxygen consumption scales as mass to the 2/3–8/10 power. This fundamental principle explains why the appropriate drug dose per kilogram of pet cat is higher than that of an average adult human, and why the cat's resting heart rate is over 140 beats min−1 when my own is closer to 70 beats min−1, and a large whale's is closer to 15 beats min−1. The scaling pattern holds in endotherms and ectotherms alike. Yet, in spite of the tremendous utility of metabolic scaling, the cause of this phenomenon remains elusive.
James Gillooly and colleagues at the University of Florida, Gainesville, used another fundamental principle of comparative physiology to look into one possible driver of metabolic scaling: Fick's law of diffusion. Passive diffusion of oxygen into the body may be a rate-limiting step in aerobic metabolism and, as the first step in the process, seemed a likely candidate. According to Fick's law, the rate of passive diffusion across a membrane is proportional to the surface area of that membrane, and inversely proportional to the thickness of the membrane. Given this relationship, if you know how membrane surface area and thickness relate to mass, you can relate passive diffusion capacity to mass directly.
Gillooly and his team compiled data on respiratory membrane surface area and thickness for a range of vertebrates, including animals from all major vertebrate classes, with representatives from all ecosystems and all forms of locomotion. This is particularly remarkable for the amphibians included in the study, as they obtain oxygen through their mouths and skin in addition to their lungs. Once the team had this information, they found that respiratory surface area scales with mass strongly, whereas membrane thickness changes little with body size.
Using the scaling exponents calculated from the published data, and estimates of the physiological properties of respiratory membranes, the researchers applied Fick's diffusion equation to model how passive oxygen diffusion capacity varies with mass. Doing so revealed that the relationship between oxygen diffusion capacity and body size was statistically indistinguishable from the relationship between resting oxygen consumption and metabolic rate for both endotherms and ectotherms. In other words, the body's capacity for passive oxygen diffusion precisely matches its resting metabolic oxygen requirements. This supports the idea of symmorphosis, a hypothesis suggesting that no one bodily system is over-engineered relative to the others.
The researchers noted that the match between resting oxygen consumption rate and diffusion capacity is inconsistent with the idea that respiratory systems evolved to optimize performance at maximum activity levels: it would appear instead that the respiratory surface is acting at capacity during resting activity and that the jump between resting and active metabolic rate could be made by modifying the oxygen partial pressure gradient over the respiratory surface, consistent with their model.
It may be a jump to suggest that oxygen diffusion capacity is the rate-limiting step in oxygen consumption, but Gillooly and colleagues present intriguing evidence of a structure–function match: a step in the right direction on the path to explaining the existence of metabolic scaling. Of course, only time will tell whether the symmorphosis hypothesis will hold for other components of the metabolic pathway.