From Cells To Whales: Universal Scaling Laws In Biology

Working with biologists James Brown of the University of New Mexico and Brian Enquist of the Santa Fe Institute, West has put together a set of seemingly simple principles to form a theory that explains the universal scaling laws of biology. With applications from cells to whales, these scaling laws have the potential of placing life on earth in a mathematical context. Simply put, the universal scaling laws of biology are a set of workable constraints that mathematically explain the amazing structure, function and variety of living things. The theory proposed by West and his colleagues, presented today at the 1999 American Association for the Advancement of Science Annual Meeting, predicts such things as the structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks. In particular, their theory explains the origins and ubiquity of a set of mathematical laws known as the quarter-power scaling laws, observed to link traits of plants and animals.

According to West, "life is the most complex physical system in the universe. Beyond natural selection, genetic codes and the like there are hardly any general principles or laws that we know that it obeys. Scaling laws are the exception. These are quantitative laws and, remarkably, they are absurdly simple given you are dealing with the most complex of systems."

The model proposed by West and his collaborators is based on the idea that a common mechanism underlies life ­ the transportation of materials though linear networks that supply all parts of an organism. These transport systems, whether mammalian blood vessels or plant vascular systems, are, in turn, based on three unifying principles.

West explains, "first, in order for the network to supply the entire volume of the organism the network system needs to have a space-filling, fractal-like branching pattern. Second, the final branch of the network, such as a capillary in the circulatory system, must be size-invariant, which means it is the same size in every organism. For example, the capillary in a mouse is the same size as one in a lion. Finally, the energy required to distribute resources is minimized. In other words, the distribution networks that have evolved in living systems must use the minimal amount of energy required to keep it alive."

These three principles, taken together, might explain the nature of the universal scaling laws of biology, but perhaps the most exciting part of the findings is that scaling laws seem to work at many levels. In fact, it works as well at the cellular level and below as it does at the multicellular level. In seeking to expand the work, West is now working with other scientists to investigate whether or not these scaling laws might also apply to such diverse entities as river systems, which bear a striking similarity to circulatory systems, and to large corporations. From whales to cells, there seems to be no end in sight for the potential application of these laws.

Los Alamos National Laboratory is operated by the University of California for the U.S. Department of Energy.