Local optimization of oxygen transport gives rise to Kleiber's law

For nearly a century, scientists have puzzled over the physical cause of metabolic scaling. Metabolic rate, the energy an organism uses, scales differently depending on the size of the creature. Small organisms follow a straightforward proportion between metabolism and body mass, but larger animals adhere to Kleiber's three-quarter-power law.

In a breakthrough study, researchers have now derived both of these behaviors from a concept known as the Metabolic Holon (MH). The MH is a locally optimized capillary-tissue unit that optimizes the supply of oxygen through a combination of convection, diffusion, and cellular consumption. This physical similarity suggests that the effective number of repeated MHs remains constant within metabolic groups, regardless of the organism's overall size. However, the magnitude of this number differs among groups.

Remarkably, this theory predicts absolute metabolic rates across a vast range - spanning 18 orders of magnitude. It also accounts for the transition between the two distinct metabolic scaling regimes, as well as the variation in group-specific levels. Furthermore, heart-rate scaling is also predicted by the theory, without requiring calibration against any metabolic-rate or heart-rate data.

An empirical constraint based on lifetime and heartbeat sets the limit for lifespan. In essence, Kleiber's law emerges as one asymptotic consequence of a broader physical theory governing aerobic metabolism in organisms.