GUTs in biology?

Abstract

A recent book charts the history of metabolic scaling laws. Is this a place to look for a grand unified theory in biology? Florian Maderspacher reports. A recent book charts the history of metabolic scaling laws. Is this a place to look for a grand unified theory in biology? Florian Maderspacher reports. Scientific progress involves an interplay of theory and empiricism. Scientists gather facts, discover principles behind the facts and build a theory. They test theories by gathering more facts that can lead to confirmation or modification of the theory or to its abandonment. Ideally, theory and empiricism inspire each other, but in reality they often are at odds — not least because different scientists prefer being one or the other, either empiricists or theorists. Particularly in biology, theory and empiricism have not always been balanced. For centuries, biology mainly meant collecting and describing an ever growing array of animals and plants, whose diversity and beauty bewildered scientists. This changed with the advent of evolutionary theory — the first grand unified theory (GUT) in biology. Like any good theory, evolution built on a wide range of observations and made far-reaching predictions. In the 20th century, the mechanisms of heredity and population genetics were integrated into the evolutionary equation. With the elucidation of the mechanisms of how genetic information is transmitted and built into an organism, a framework emerged that could perhaps be called an ‘informational theory of life’. It is a powerful and well-established grand unified theory of biology and — as many would argue — the only one. Another place to look for unifying principles in biology is the chemical and physical basis of life —in particular metabolism. The notion that life is based on processes that can be described in physical terms was the kiss of death for vitalism. It brought biology closer to sciences, such as physics and chemistry, that are governed by laws that can be formulated mathematically. But the chemical reactions within organisms could be described in much the same way as if they occurred in a test tube, and a biology-specific theory of metabolism seemed to be missing. The recent book ‘In the Beat of a Heart’ by John Whitfield deals with precisely this —the quest for a unified theory of metabolism and energy in biology. Unlike biology, physics in the 20th century has been largely theory-driven. In fact, some fields of physics, such as string theory, make do without virtually any empiricism. This difference between physics and biology has been the source of many a joke and of substantial superiority and inferiority complexes in both camps. Whitfield's book starts with D'Arcy Thompson, who attempted all his life to explain biology — in particular the shapes of organisms — in physical and mathematical terms. However, 90 years later, the yield is fairly meagre. Despite a detailed understanding of the genetic programs that build an organism, their quantitative aspects are still poorly understood and a unified theory of growth and form still seems far away. So, where else might a unified theory of biology be found? In his book, John Whitfield portrays an eclectic set of biologists — some of them ‘converted’ physicists — who study metabolism. The story begins with Max Rubner, who in the 1880s began measuring the metabolic rates of dogs with unprecedented accuracy. He found that while large dogs burn more energy, their relative metabolic rate is lower than in small dogs. His measurements led him to conclude that the metabolic rate of an animal increases approximately with its mass raised to the power of 2/3. Rubner reasoned that the amount of energy an animal burns increases with its surface area. The exponent of 2/3 thus matches the exponent by which surface area and volume of a body increase when that body is enlarged by a given factor: If the sides of the cube are doubled, the surface area increases by 4 (22), while the volume increases by a factor of 8 (23). Rubner's so-called ‘surface law’ stated that the relative metabolic rate of a given animal decreased with the same rate as its surface-to-volume ratio. This idea was nicely in tune with the principle of allometric scaling: Different properties of an organism scale differently. This is why, for instance, larger animals have proportionally thicker legs — ironically, a fact first noted by a physicist, Galileo Galilei. However, Rubner did not actually measure the surface areas of his subjects. While body mass was easy to measure, surface measurements proved to be incredibly tricky. Human subjects were initially wrapped in tin foil or paper to infer surface area. Later on, photography, plaster, paraffin wax or paint rollers were used (Figure 1). Whitfield gives an entertaining account of how complex such seemingly trivial measurements can become; unlike physics, biology doesn't deal with ideal geometric bodies, but with bodies that have pointy ears or prickly legs. In the 1920s, the Swiss emigrant Max Kleiber began measuring the metabolic rates of a number of other mammals and found that metabolic rate actually scales with body mass raised to the power of 0.74. As more and more creatures — birds, reptiles, insects and eventually unicellular organisms — had their metabolic rate and body mass measured, the values came out close to Kleiber's exponent. In 1963, a value of 0.75 was adopted by a vote at a conference, mainly because this value was handier to work with. Kleiber's law of metabolic rate being equal to a constant times body mass raised to the power of 3/4 has since then become part of the biology canon. But what looks like a success story of a general law in biology equally reflects the difficulties of turning biology into an exact quantitative science. At a time when physicists measured many parameters down to the tenth decimal, biologists were (and are still) arguing about a straightforward measurement. The exponent has always had a checkered history, full of wishful tweaking: Rubner's metabolic-rate measurements actually yielded a value of 0.61; but the 2/3 value just seemed to fit the geometrical scaling laws so much better. And up to now, the values obtained range between 0.61 and 0.76 — imagine the state of physics had it such variation in principal constants. Part of the variation depends on the species used. It turns out that in Kleiber's times preferentially large herbivores were measured, which may have increased the value of the coefficient. A more balanced set of species may in fact yield a value closer to Rubner's 2/3. As with the surface measurements, the devil is in the detail. Whitfield's history of Kleiber's law may thus be equally well read as a cautionary tale of how biology may actually be fundamentally different from physics. If you accept these principal uncertainties, however, it is hard not to be intrigued by the power of Kleiber's power law. For one, the correlation holds over an impressive 20 or so orders of magnitude — from microbe to mammoth. It is true for plants, too. And when other parameters in biology were investigated, similar relationships kept cropping up. And not only that, they kept cropping up with exponents that are multiples of quarters: Life span in a wide range of animals increases with body mass raised to the power of 1/4 and heart rate scales with mass raised to the power of −1/4. Similar scaling relationships are found at the bottom of the size range of life — at the cellular and subcellular level — and at the very top end — at the levels of populations and ecosystems; for instance, the population density of a given species decreases with its body mass raised to −3/4. A great merit of Whitfield's book is its gathering and explication of the evidence for power laws across all of biology. The enticing thing about these power laws is their explanatory scope, both in terms of the range of organisms and the number of processes. And they are amazingly simple, even for the notoriously mathematically under-skilled biologists. Eventually, they can be written as: Y = Y0Mb, where Y is a biological parameter (say, life span), Y0 is a normalisation constant, and M is body mass. Such a simple and yet broad relationship seems like the ideal candidate for a grand unified theory of biology, so is Y = Y0Mb the E = mc2 of biology? As we follow Whitfield's narrative of the power law as a unified principle, the question arises of what is the underlying cause for the observed relationships. Why do they almost always come in quarters? Apart from describing relationships between parameters, what do they explain? ‘In the Beat of a Heart’ follows the trail of a group of scientists who have tried to answer these questions. Geoff West, Jim Brown and Brian Enquist formulated their ideas in a paper that since its publication ten years ago has kick-started a flurry of high-profile controversy (West, G.B., Brown, J.H., and Enquist, B.J. (1997). A general model for the origin of allometric scaling laws in biology. Science 276, 122–126). Not surprisingly, the father figure of that movement, Geoff West, is a physicist who has developed an interest in biology. West's grand idea — as clearly explained in Whitfield's book — is that it is all about how energy is distributed in organisms. If you take an animal, energy in the form of nutrients and oxygen is dispatched by lungs (Figure 2) and blood vessels. According to West's theory, it is the properties of these networks that give rise to the power-law relationship between body mass and metabolic rate. Examples of such networks include the vascular systems of plants and animals, but the concept can also be extended to subcellular distribution networks or the flow of energy in ecosystems. All of these networks have the properties of a fractal, a concept best known from the Mandelbrot set, an icon of 1980s geekdom. Mathematical fractals are self-similar; they follow similar patterns independent of scale, which is why complex fractal patterns can be generated from relatively simple rules. But unlike mathematical fractals, biological fractals cannot be scaled down infinitely; there is a minimum size. For instance, a capillary needs to be just big enough to allow blood cells to pass through. These fractal networks are space-filling and minimised by natural selection to enable the most efficient energy distribution. Modelling the geometry of vascular networks and the flow within them, West and his colleagues described that the quarter power-scaling emerges from the constraints imposed by the geometrical properties of a fractal network. The networks limit the amount of energy that can be distributed, giving rise to the link between size and metabolic rate. As a body grows, the number of capillaries and the area they can supply becomes limiting, thus slowing down metabolic rate. Whitfield's accomplishment is to explain this theory accessibly to math ignoramuses; the book is thus an ideal read for biologists. It is interesting that West's theory is formally similar to Rubner's surface law, which described the scaling of a two-dimensional property (surface area) with a three-dimensional one (body size). In that sense, the fractal theory of metabolic scaling describes the scaling of a three-dimensional property in a hypothetical fourth dimension. Starting from the mammalian vascular system, West and his group have in the past ten years continuously expanded their theory both in scale and scope: from the subcellular level to populations; from body mass to developmental growth, ageing and mutation rates. In many of these relationships, invariant quantities keep emerging: the life span of mammals, for instance, increases with mass raised to 1/4, while heart rate decreases with mass raised to −1/4; thus, the number of heart beats in life remains more or less constant for all mammals. The idea that the pervasive quarter power relationships reflect the properties and constraints of energy flow through a system is tantalising, but has at the same time stimulated intense criticism — a fact not always obvious in the book. Taking things further, ‘In the Beat of a Heart’ quite literally trails off to the woods and explores how the metabolic-networking theory can be applied to ecology. At first, it seems odd to look for unifying principles in an environment as messy and as uncontrollable as a Costa Rican rainforest, rather than in a lab, especially as the scaling theory makes predictions that could be rigorously tested in a more reductionist setting. But after all, it was ecologists, such as Jim Brown and Brian Enquist, who midwifed the theory in the first place. Not surprisingly, power laws are everywhere in ecology. They describe the phenomenon of self-thinning — that there are fewer big animals or plants per area than small ones. Population density decreases roughly with body mass raised to the power of −0.75. Again, a similar principle of energy invariance shines through: As the metabolic rate scales with body mass raised to 0.75, this means that the amount of energy the members of a given population can extract from a given area remains roughly constant. Ultimately, the book tries the theory of scaling on one of the oldest and hardest chestnuts in biology — the problem of why the number of species increases as you move towards decreasing latitudes. This problem has been puzzling people since the times of Alexander von Humboldt, to whom the books pays nice homage. Again, distributions of species numbers follow a power law; however, the underlying causes are not as easily grasped and likely to be complex — illustrating the limitations of grand unified theories in biology. So, is metabolic scaling a candidate for a grand unified theory in biology? Whitfield's book is happy to leave that question open. After all, it is perhaps at its heart a mainly physical theory. It deals with a physical parameter — energy — and explains how its distribution constrains and influences biology. This is pretty much what D'Arcy Thompson had in mind — an interface between physics and biology. Whitfield's accomplishment is to provide the first accessible introduction into how metabolism might be a common denominator connecting the two. It might well serve to stimulate people outside ecology in other, more reductionist fields of biology to put the theory of metabolic scaling to a test. Rather than a carefully balanced account of its pros and cons, ‘In the Beat of a Heart’ offers a glimpse into the breadth of biological phenomena metabolic scaling can describe. It can be read as an introduction into the theory, as a history of science and scientists, and a story of a science in the making. Whether or not this can be a ‘theory of everything’ — something that even physics has not accomplished — remains to be seen. Perhaps it could at its best become a ‘theory of everything, but’. As even the proponents of the theory acknowledge — and is the case so often in biology — it may be the exceptions rather than the rule that are most promising to study. It was Immanuel Kant who stated that it is “absurd […] that perhaps some day another Newton might arise who would explain to us, in terms of natural laws unordered by any intention, how even a mere blade of grass is produced.” ‘In the Beat of a Heart’ conveys the good news that this position is still up for grabs.