Disproportional fraction of inactive components leads to the variation in metabolic scaling

In biological systems, solitary organisms or eusocial groups, the metabolic rate often scales allometrically with systems’ size, when they are inactive, and the scaling becomes nearly isometric when the systems are active. Here I propose a hypothesis attempting to offer a departing point for a general joint understanding of the difference in the scaling powers between inactive and active states. When the system is inactive, there exist inactive components, which consume less energy than the active ones, and the larger the system is, the larger the fraction of the inactive components, which leads to sublinear scaling. When the system is active, most inactive components are activated, which leads to nearly isometric scaling. I hypothesize that the disproportional fraction of the inactive components is caused by the diffusants screening in the complex transportation network. I.e., when metabolites or information diffuses in the system, due to the physical limitation of the network structure and the diffusant’s physical feature, not all the components can equally receive the diffusants so that these components are inactive. Using the mammalian pulmonary system, ant colonies, and other few systems as examples, I discuss how the screening leads to the allometric and isometric metabolic scaling powers in inactive and active states respectively. It is noteworthy that there are a few exceptions, in which the metabolic rate of the system has an isometric scaling relationship with size at rest. I show that these exceptions not only do not disapprove the hypothesis, but actually support it.