This work sits within a line of research seeking the physical foundations of metabolic scaling. Nearby are studies on why a mouse runs hotter than an elephant, how cells choose the path to fluidity, and how curvature dictates cell size. All of them try to connect local transport processes with whole-organism properties. This paper goes a step further: it does not merely derive the exponent, it predicts the absolute level of metabolism and the transition between regimes.
The authors build their theory around the metabolic holon, the minimal functional unit consisting of a capillary and the surrounding tissue. For each holon an optimization problem is solved: minimize vessel material and viscous losses while maximizing oxygen extraction. This yields Murray's relation between flow and vessel diameter. The second condition, full oxygen utilization, fixes the capillary length. The holons are then repeated N times to form an organism. The number N is taken as constant within a metabolic group (for endotherms, N ≈ 5×10⁸). Parameters come from independent sources, with no fitting to metabolic data.
The theory reproduces metabolic data across 18 orders of magnitude with R² = 97.7%. For small organisms, where diffusion dominates, a linear dependence on mass is predicted. For large ones, a power law with exponent 3/4. The transition occurs at the mass where diffusion time equals reaction time. The theory also predicts heart rate (R² = 0.95) and lifespan (R² = 0.92) in endotherms. The ratio of holon numbers in endotherms and ectotherms (~10⁴) gives roughly a tenfold shift in metabolic level between the groups.
Unlike neighboring studies that focus on a single level of organization (cell, tissue or organism), this theory links all three levels through a mesoscopic holon. It is the first to derive absolute values of metabolic power, not just exponents. The key difference is its prediction that the number of holons stays invariant during growth within a group: an increase in size is achieved by enlarging holons, not by adding new ones. This separates organismal growth from evolutionary changes in transport organization.
The theory opens a path to testing in specific organisms: one can measure the number of functional units in different species and compare with the prediction. Another direction is accounting for tissue heterogeneity and nonlinear oxygen binding. The approach might extend to other transport systems, for example in plants or fungi.
The results matter for comparative physiology, evolutionary biology and ecology. They provide a tool for estimating the metabolic needs of extinct species from body mass.
Test the invariance of holon number with direct measurements of the microvascular network in animals of different sizes. Investigate how the holon number changes during ontogeny and adaptation to hypoxia.
The work directly addresses the unsolved problem of the origin of Kleiber's law. It proposes a physical mechanism linking cellular oxygen consumption to whole-organism metabolism and offers testable predictions for future experiments.
A shrew's heart beats at about 1000 beats per minute, while a whale's beats only 10-20 times. The theory explains this difference through the number of holons and the volume of blood the heart must pump per beat.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.