Do Energy Transport Systems Shape Organisms?

Research Research: Do Energy Transport Systems Shape Organisms? By Steve Bunk Brian Evans/lightSpace BEAUTY OF LIFE: This computer-generated image illustrating how organisms grow proportionally represents only a tiny portion of image E on the following page. Could it be that the way organisms transport resources is the most pervasive influence on biological structure and diversity? Curious though it may seem, recent research suggests that networks for transporting the materials essential

By | December 7, 1998


Research: Do Energy Transport Systems Shape Organisms?

By Steve Bunk

Brian Evans/lightSpace

BEAUTY OF LIFE: This computer-generated image illustrating how organisms grow proportionally represents only a tiny portion of image E on the following page.

Could it be that the way organisms transport resources is the most pervasive influence on biological structure and diversity? Curious though it may seem, recent research suggests that networks for transporting the materials essential to life may be a prime mover in determining shape and form in nature.

This is the fundamental tenet of a framework for explaining many features of biological diversity that is being developed by three scientists: Geoffrey B. West, a theoretical physicist at Los Alamos National Laboratory in Los Alamos, N.M.; James H. Brown, a biology professor at the University of New Mexico; and Brian J. Enquist, a postdoctoral biologist at the nonprofit Santa Fe Institute.

A paper published by the trio in September1 has supplemented the researchers' first paper, published last year,2 and others are in preparation. Brown and West also are editing a book, Scaling in Biology, to which all three scientists will contribute; it is scheduled to be published in 1999 by Oxford University Press. The ambitious aim is to establish that certain physical principles underlying allometric scaling laws are major determinants of changes in many anatomical and physiological variables of organisms as they increase in body size.

Body size, which varies over at least 21 orders of magnitude, from Mycoplasma to the blue whale, is central in the scaling laws of allometry, the study of evolutionary changes in the size or proportion of organisms. Many biological phenomena--such as metabolic rate, heartbeat, time of blood circulation, lifespan, and size of organismal structures such as mammalian aortas or tree trunks--scale at quarter-powers of body mass. Quarter-power scaling has long been recognized as prevalent in nature, but the relationship of body size and physiology has eluded biologists for decades.

The first paper by West and colleagues presented a general model for the origin of allometric scaling laws in biology. "I think the major accomplishment of this, in a certain sense, is that here's this plethora of scaling laws ... and they cover all life, but they all derive from the same set of principles," West explains. "And we're all constrained by that. But [the model] goes much further and says not only are we constrained as we develop, we're constrained as we evolve."

Enquist adds, "It's amazing that some very simple beginning points in the model--just three general principles--not only can be applied to the mammalian cardiovascular system, but also to plants, insects, possibly all life."

The model's three general principles stem from the observation that living things have a common mechanism of transporting life-sustaining materials through a linear network that branches to supply every part of the organism. The first two principles are that a space-filling, fractal-like branching pattern is necessary to supply the organism with what it needs to live, and that the final unit of this branching pattern is always the same size. As West has put it, "When it comes to energy-transport systems, everything is a tree."

James H. Brown and Geoffrey B. West
The third assumption is that the energy required by the transport system is minimized. This principle recognizes the importance of natural selection to evolutionary development, yet it emphasizes the optimization inherent in that process. It asserts that what is optimized is not only competition with others for available resources, but also how well the individual uses those resources.

"The vast majority of what you see around you--not the details, but the vast majority--is governed by these principles," says West. The principles "seem to be at work at all levels, and they manifest themselves as this myriad of laws, all of which have quarter-power. And they manifest themselves not just between organisms, but within an organism."

Perhaps the most fundamental scaling law is the metabolic rate of organisms--the amount of energy used to sustain life--which is known to be proportional to body mass raised to the power of 3/4. Why this 3/4 exponent or any of the innumerable quarter-power scaling laws should hold true, has not been clear. The quantitative model by West and colleagues not only explains the origin and prevalence of quarter-power scaling, it establishes its own general validity by successfully predicting the size of essential features relative to body mass in such disparate transport systems as mammalian blood vessels, plant vascular systems, and insect tracheal tubes.

The 1997 Science paper by West et al. demonstrates that quarter-power scaling exponents of body mass are predictable for 26 variables in mammalian cardiovascular and respiratory systems--such as radius of the aorta and trachea, velocity of blood and air, and cardiac and respiratory frequency--showing only occasional, small deviations when compared to empirical observations. The recent paper in Nature extends this work into plant ecology. For 12 orders of plant magnitude, it shows that the rate of energy use of individuals determines plant density in a given environment. This contradicts the traditional "thinning law," which states that the geometric volume and area filled by individual plants is what determines how many plants can occupy a field or forest.3 Enquist and colleagues have shown that a plant's ability to crowd out others in competition for resources is not what determines density. Rather, the ability of the individual plant to use available resources, regardless of its size, is what counts.

Neither the old nor the new model can predict what sizes and densities of plants will occur as the plant population thins in an agricultural field or other environment. But the new model demonstrates that, both within single species and across different species, plants of all sizes can achieve the same rates of local resource use, just as animals can. This principle, called energy equivalence, "may thus be one of the most widespread of ecological regularities," University of Santa Barbara evolutionary biologist John D. Damuth wrote, also in the Sept. 10 Nature.4

Damuth cautions that the model is general, and needs to be bolstered by more empirical studies. The mathematical relationship between population density and metabolism across taxa is not a coincidence, he says. "What we don't understand is why there should be that relationship." Density scaling is not simply a question of metabolism, he thinks, because the extra variable involved is how much energy is available. What prevents evolution from producing species that violate the energy equivalence relationship?

"Only a very few variables determine much of what's happening," West says. "The fact that you're competing out there plays a relatively minor role in much of this." Nevertheless, he acknowledges that theirs is a "Garden of Eden model," because as organisms grow to maximal size, competition for food does become increasingly important.

All figures by Brian Evans/lightSpace
BRANCHING AND SCALING: The small box in each of the above images illustrates the next generation of organism growth, as magnified consecutively in pictures A through E.

A paper they now are drafting applies the general principles to resource transport in plant vascular networks. It makes numerous predictions for allometric exponents and includes calculations showing that the maximum height of trees is about 100 meters, due to hydrodynamic and biomechanical constraints. Future work will address maximal size for mammals living on land, although that will be more complex because of the biomechanics of motion. Competition for food plays a significant role, West says.

Another way the model is idealized is that complications such as irregularities of vessels, turbulence, or nonlinear effects are seen as having only minor impact on the dynamics of a distribution network. Nor is the fractal branching of the network consistent in all organisms at all phases of development. For example, blood vessel development in embryos does not follow an exact fractal pattern. But a paper published after the general model was introduced confirms that deviations from perfect fractal geometries do not appreciably change the predictions and applications of the model.5

Another goal is to show that quarter-power scaling extends to 27 orders of magnitude, beyond the unicellular level into the respiratory complexes of cellular mitochondria. Presumably, the same physical mechanisms arising from the scaling laws would be at work in the mitochondria, though they wouldn't have distribution systems that look like, say, circulatory systems. The researchers hope to find out what the network does look like, and how energy is transported within mitochondria. They are working on this project with Los Alamos biochemist William H. Woodruff, who will help to structure experiments that can demonstrate the viability of the intracellular model once it is completed.

So far, the team suspects that the cell and the interior of its mitochondria could have hierarchical branching in their diffusion surfaces, through which nutrients and energy are transported. They have shown that mitochondrial density scales at the organismal mass to the minus one-quarter power, and they hope to determine how the cell's surface area scales with its mass. As the final branch of the network, the respiratory complex is size-invariant; West says this implies that mitochondria also are size-invariant. However, as the scale ascends from that level, cells do not have to have the same metabolic rate, a variance that is accommodated by their model.

Practical applications of the model could involve the introduction of major deviations, such as replacing some of the uniform elasticity of the tubes with hardening or blockage, as in cardiovascular conditions. Theoretically, the researchers could even devise technical tools to pinpoint embolisms noninvasively, based on measurements. They say they have been approached by "the cardiovascular community" to do such work, and officials at the National Institutes of Health have asked them about developing pharmacology and toxicology models.

But finding time is the problem. "I would not feel satisfied with this work until we have a fundamental theory of aging and death," West suggests. "Lifespan also has a quarter-power scaling, and it's hard to believe that this isn't connected to all these other laws." Enquist interjects, "The number of heartbeats of a shrew and an elephant is the same." During aging, energy is dissipated and entropy is produced, making the system less ordered. The body's repair mechanisms fight against the effects. The entire process can be understood in terms of scaling laws, they believe.

The three regard their work as something of a historical throwback. West notes that the term "allometry" was introduced by English biologist Julian S. Huxley in his 1932 book, Problems of Relative Growth.6 A number of good books were written about allometric scaling through the early 1980s, he says, but once the laws were classified, little further progress was made in understanding them, leading to a decline in interest during the late 1980s. Given the rise to prominence of molecular biology and genetics, he thinks a "cultural paradigm shift" may now be necessary for biologists to forgo focusing on the details of variation or diversity in individual organisms until they are familiar with the underlying unification principles inherent in the scaling laws.

Enquist agrees that although their work has caused a stir among those familiar with allometry, it has not yet caught on widely among other biologists. "I don't really think biologists appreciate that these scaling relationships with body size really do ramify into everything they study. From that [standpoint], I think it's very easy to get into," he remarks. "Unfortunately, the emphases placed on whole, organismal biology and comparative biology are more at the molecular end."

Indeed, the apparent slowness of some biologists to embrace this model may be partly due to the relatively complex mathematics involved, though the scaling laws themselves are fairly simple exponential equations. "For a biologist to get involved and use these techniques," West acknowledges, "requires a major commitment."

Steve Bunk is a contributing editor for The Scientist

  1. B.J. Enquist et al., "Allometric scaling of plant energetics and population density," Nature, 395:163-5, Sept. 10, 1998.

  2. G.B. West et al., "A general model for the origin of allometric scaling laws in biology," Science, 276:122-6, 1997.

  3. K. Yoda et al., Journal of Biology Osaka City University, 14:107-9, 1963.

  4. J.D. Damuth, "Population ecology--Common rules for animals and plants," Nature 395:115-16, Sept. 10, 1998.

  5. D.L. Turcotte et al., "Networks with side branching in biology," Journal of Theoretical Biology, 193:577-92, August 1998.

  6. J.S. Huxley, Problems of Relative Growth, London, Methuen, 1932.

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