A general model for metabolic scaling in self-similar asymmetric networks

Alexander Byers Brummer, Van M. Savage, Brian J. Enquist

Research output: Research - peer-reviewArticle

  • 1 Citations

Abstract

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.

LanguageEnglish (US)
Article numbere1005394
JournalPLoS Computational Biology
Volume13
Issue number3
DOIs
StatePublished - Mar 1 2017

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Scaling
Model
Body Size
allometry
Biological Evolution
Biodiversity
Cardiovascular System
Blood Vessels
Allometry
Biological Networks
body size
prediction
organism
branching
organisms
Branching
Prediction
cardiovascular system
physiology
asymmetry

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Modeling and Simulation
  • Ecology
  • Molecular Biology
  • Genetics
  • Cellular and Molecular Neuroscience
  • Computational Theory and Mathematics

Cite this

A general model for metabolic scaling in self-similar asymmetric networks. / Brummer, Alexander Byers; Savage, Van M.; Enquist, Brian J.

In: PLoS Computational Biology, Vol. 13, No. 3, e1005394, 01.03.2017.

Research output: Research - peer-reviewArticle

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