A general model for metabolic scaling in self-similar asymmetric networks.
How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber's Law can still be attained within many asymmetric networks.
Department of Physics, University of Arizona, Tucson, Arizona, United States of America.|Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona, United States of America.
Alexander Byers
0000-0002-8776-0939
AB
Brummer
Department of Biomathematics, UCLA David Geffen School of Medicine, Los Angeles, California, United States of America.|Department of Ecology and Evolutionary Biology, UCLA, Los Angeles, California, United States of America.|Santa Fe Institute, Santa Fe, New Mexico, United States of America.
Van M
VM
Savage
Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona, United States of America.|Santa Fe Institute, Santa Fe, New Mexico, United States of America.
Brian J
BJ
Enquist
D049628:Body Size; D003198:Computer Simulation; D004734:Energy Metabolism / Q000502:physiology*; D064688:Metabolic Flux Analysis / Q000379:methods*; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D008954:Models, Biological; D015398:Signal Transduction / Q000502:physiology*