Heterogeneity of cells may explain allometric scaling of metabolic rate.

The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.