DOE Human Genome Program Contractor-Grantee Workshop VIII
February 27-March 2, 2000  Santa Fe, NM

155. The Tree of Life: The Origin of Universal Scaling Laws in Biology from Molecules, Genes, and Cells to Whales Cells to Whales

Geoffrey B. West¹, James H. Brown², Brian Enquist³, and William H. Woodruff⁴

Los Alamos National Laboratory and Santa Fe Institute¹, University of New Mexico and Santa Fe Institute², University of California, Santa Barbara³, and Los Alamos National Laboratory⁴

gbw@lanl.gov

Although life is the most complex system known, many of its attributes satisfy remarkably simple universal scaling laws. For example, metabolic rate scales as mass to the 3/4 power, ranging from the largest organisms (whales and sequoias) to the very smallest unicellular microbes, even extending down through mitochondria to the molecular level of the respiratory complex - an astounding 27 orders of magnitude. Many other such allometric scaling laws are known which relate lengths (such as the radius of the aorta, genome size) and time-scales (heart-rate, lifespan, reaction rates) to mass. These are typically power laws whose exponents are simple multiples of 1/4. The phenomenology of these observations will be reviewed and a general model presented that explains quantitatively their origin and universality. It is based on the fundamental observation that, at all scales, life is sustained by the transport of resources and information through space-filling fractal-like hierarchical branching networks whose terminal units are invariant. Assuming that natural selection has led to network systems which minimize energy dissipated, or, alternatively, to the area of interface with the resource environment being maximized, the origin of quarter-power scaling for a myriad of observables for diverse biological systems can be explained. A general argument will be presented augmented by detailed analyses of the mammalian circulatory and plant vascular systems, for which complete quantitative descriptions can be derived. The extension of these ideas to growth, aging and possibly genomics will be dicussed.