In a paper published in the April 4 issue of Science,Geoffrey West of Los Alamos National Laboratory and his colleagues James Brown and Brian Enquist at the University of New Mexico for the first time present a general model that predicts essential features of transport systems, such as vertebrate cardiovascular and respiratory systems, plant vascular systems and insect tracheal tubes. The model offers profound implications for macroscopic aspects of biology.
At Los Alamos, West was applying his high-energy physics background to the mystery of why all animals, regardless of body size, obey the same simple scaling law for metabolic rate - a measure of how much energy an organism consumes per second to maintain life. The answer, he believed, was essential to understanding how evolution maximizes fitness.
An animal 100 times larger than a mouse will not have a metabolic rate 100 times higher, as might be expected since it has so many more cells to feed. Its metabolic rate will, in fact, be only about 30 times higher in this case, following a consistent and predictable formula. The law governing this, known as Kleiber's Law, had been around for decades, but no one understood the reason for it, West said.
For their part, Brown and Enquist were trying to solve the riddle of why the metabolic rate of plants exhibits the same proportional scaling phenomenon observed in animals. As ecologists, they were interested in determining how population densities were related to the biological laws that govern individuals. Like West, they predicted that scaling laws arose from a common underlying mechanism: living things are sustained by the transport of materials through a branching network.
In a collaboration under the auspices of the Santa Fe Institute, the three scientists combined a background in physics and calculations with the ecologists' intuition about living systems to study these universal scaling laws.
The researchers built their model on three assumptions: First, a space-filling, progressively branching pattern is required to supply life-sustaining fluids to all parts of any organism. Second, the final branch of the network - the veins in the leaves of a tree or the capillaries of a circulatory system - are the same size regardless of a species' body mass. And, third, the energy used to transport resources through a living network is always minimized.
The first assumption came from the researchers' observation that a space-filling branching network, or fractal, is a natural structure for transporting nutrients to every cell in an animal's body. Thus, all the cells in the human body are fed regularly through the cardiovascular system, which transports oxygenated blood through the aorta into major arteries and through smaller, branching arteries to capillaries, each of which feeds a few cells.
This fractal branching network is universal in living systems. Cardiovascular systems, respiratory systems, plant vascular systems and even river systems are all examples of fractal branching networks.
"When it comes to energy-transport systems, everything is a tree," West said.
The second assumption arose from the researchers' knowledge that all living cells, regardless of an organism's species or body weight, are about the same size. For example, the capillaries in cardiovascular systems and end bronchial tubes in mammalian respiratory systems are the same size in all animals.
"You and the mouse are made of the same stuff," West said.
Because cells are the same size, capillaries must be the same size to bring nutrients to all cells. Systems built from similar cellular foundations will operate within the same laws of scale. So the metabolic rate of a mouse follows the same rules as the metabolic rate for all other mammals, including humans. Thus West's scaling model may become a new analytical tool in testing of pharmaceuticals, allowing researchers to better predict certain effects of chemicals on humans based on laboratory animal studies.
Lastly, living systems minimize the energy required to transport resources. And the most efficient transport system, it turns out, is a fractal branching network. The smallest fraction of the system must be a miniature replica of the entire network, the only difference between the two being one of scale.
"You are a walking fractal," West said. "It would appear that evolution strives to make organisms as efficient as possible."
Based on these assumptions, the model accurately predicts the structural and functional properties of the mammalian cardiovascular and respiratory systems. For example, given the body mass of an adult male, the model can calculate the length and cross-sectional area of his aorta. The researchers plan to test other predictions, but their work so far suggests that the scaling law is perhaps the single most pervasive theme underlying all biological diversity.
Returning to his original avenue of investigation, West sees implications for the study of evolution.
"Models of evolution must incorporate constraints implied by scaling laws," West said. "Evolution will produce fractal systems, and fractals impose certain constraints and limits."
The researchers suggest the model holds ramifications for diverse phenomena from post-embryonic growth of a single organism to the balance of population densities.
"Here is this curious law that the whole of life obeys," West said, "yet no one has thought through what the universal phenomenon of fractal structure implies for life and worked out the model."
Collaborations between physicists and biologists have altered the course of science before. In the 1950s, physicist Francis Crick and biologist James Watson collaborated on research that unmasked the double-helical structure of DNA, the twisted ladder of chemicals that serves as the blueprint for all life. Like the double-helix, the scaling law based on fractals is an elegantly simple design principle from which an infinite number of biological variations are possible.
Los Alamos National Laboratory, a multidisciplinary research institution engaged in strategic science on behalf of national security, is operated by Los Alamos National Security, LLC, a team composed of Bechtel National, the University of California, The Babcock & Wilcox Company, and the Washington Division of URS for the Department of Energy's National Nuclear Security Administration.
Los Alamos enhances national security by ensuring the safety and reliability of the U.S. nuclear stockpile, developing technologies to reduce threats from weapons of mass destruction, and solving problems related to energy, environment, infrastructure, health, and global security concerns.