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ScienceWeek
BIOPHYSICS: ON LIVING-SYSTEM SCALING LAWS
The following points are made by G.B. West and J.H. Brown (Physics Today 2004 September):
1) Do biological phenomena obey underlying universal laws of life that can be mathematized so that biology can be formulated as a predictive, quantitative science? Most would regard it as unlikely that scientists will ever discover "Newton's laws of biology" that could lead to precise calculations of detailed biological phenomena. Indeed, one could convincingly argue that the extraordinary complexity of most biological systems precludes such a possibility.
2) Nevertheless, it is reasonable to conjecture that the coarse-grained behavior of living systems might obey quantifiable universal laws that capture the systems' essential features. This more modest view presumes that, at every organizational level, one can construct idealized biological systems whose average properties are calculable. Such ideal constructs would provide a zeroth-order point of departure for quantitatively understanding real biological systems, which can be viewed as manifesting "higher-order corrections" due to local environmental conditions or historical evolutionary divergence.
3) The search for universal quantitative laws of biology that supplement or complement the Mendelian laws of inheritance and the principle of natural selection might seem to be a daunting task. After all, life is the most complex and diverse physical system in the universe, and a systematic science of complexity has yet to be developed. The life process covers more than 27 orders of magnitude in mass -- from molecules of the genetic code and metabolic machinery to whales and sequoias -- and the metabolic power required to support life across that range spans over 21 orders of magnitude.
4) Throughout those immense ranges, life uses basically the same chemical constituents and reactions to create an amazing variety of forms, processes, and dynamical behaviors. All life functions by transforming energy from physical or chemical sources into organic molecules that are metabolized to build, maintain, and reproduce complex, highly organized systems. Understanding the origins, structures, and dynamics of living systems from molecules to the biosphere is one of the grand challenges of modern science. Finding the universal principles that govern life's enormous diversity is central to understanding the nature of life and to managing biological systems in such diverse contexts as medicine, agriculture, and the environment.
5) In marked contrast to the amazing diversity and complexity of living organisms is the remarkable simplicity of the scaling behavior of key biological processes over a broad spectrum of phenomena and an immense range of energy and mass. Scaling as a manifestation of underlying dynamics and geometry is familiar throughout physics. It has been instrumental in helping researchers gain deeper insights into problems ranging across the entire spectrum of science and technology, because scaling laws typically reflect underlying generic features and physical principles that are independent of detailed dynamics or specific characteristics of particular models. Phase transitions, chaos, the unification of the fundamental forces of nature, and the discovery of quarks are a few of the more significant examples in which scaling has illuminated important universal principles or structure.
6) In biology, the observed scaling is typically a simple power law: Y = Y(sub-0)M^(b), where Y is some observable, Y(sub-0) a constant, and M the mass of the organism.(1-3) Perhaps of even greater significance, the exponent b almost invariably approximates a simple multiple of 1/4. Among the many fundamental variables that obey such scaling laws -- termed "allometric" by Julian Huxley(4) -- are metabolic rate, life span, growth rate, heart rate, DNA nucleotide substitution rate, lengths of aortas and genomes, tree height, mass of cerebral grey matter, density of mitochondria, and concentration of RNA.(5)
References (abridged):
1. T. A. McMahon, J. T. Bonner, On Size and Life, Scientific American Library, New York (1983)
2. K. Schmidt-Nielsen, Scaling: Why Is Animal Size So Important?, Cambridge U. Press, New York (1984); R. H. Peters, The Ecological Implications of Body Size, Cambridge U. Press, New York (1983); W. A. Calder III, Size, Function and Life History, Harvard U. Press, Cambridge, MA (1984)
3. K. J. Niklas, Plant Allometry: The Scaling of Form and Process, U. of Chicago Press, Chicago (1994); J. H. Brown, G. B. West, eds., Scaling in Biology, Oxford U. Press, New York (2000)
4. J. S. Huxley, Problems of Relative Growth, Dial Press, New York (1932)
5. M. Kleiber, The Fire of Life: An Introduction to Animal Energetics, Robert E. Krieger, Huntington, NY (1975)
Physics Today http://www.physicstoday.org
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Related Material:
THEORETICAL BIOLOGY: ON MATHEMATICS IN BIOLOGY
The following points are made by Robert M. May (Science 2004 303:790):
1) Darwin once wrote, "I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense." With the benefit of hindsight, we can see how much an "extra sense" could indeed have solved one of Darwin's major problems. In his day, it was thought that inheritance "blended" maternal and paternal characteristics. However, as pointed out to Darwin by the engineer Fleeming Jenkin and others, with blending inheritance it is virtually impossible to preserve the natural variation within populations that is both observed and essential to his theory of how evolution works.
2) Mendel's observations on the particulate nature of inheritance were contemporary with Darwin, and his published work accessible to Darwin. Fisher and others have suggested that Fleeming Jenkin's fundamental and intractable objections to /The Origin of Species/ could have been resolved by Darwin or one of his colleagues, if only they had grasped the mathematical significance of Mendel's results (1). But half a century elapsed before Hardy and Weinberg (H-W) resolved the difficulties by proving that particulate inheritance preserved variation within populations (2).
3) Today, the H-W Law stands as a kind of Newton's First Law (bodies remain in their state of rest or uniform motion in a straight line, except insofar as acted upon by external forces) for evolution: Gene frequencies in a population do not alter from generation to generation in the absence of migration, selection, statistical fluctuation, mutation, etc. Subsequent advances in population genetics, led by Fisher, Haldane, and Wright, helped make the neo-Darwinian Revolution in the early 20th century. Current work on the one hand provides illuminating metaphors for exploring current evolutionary problems, particularly in molecular evolution, whilst on the other hand having important applications in plant and animal breeding programs.(3-5)
4) In summary: In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because life sciences have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else.
References (abridged):
1. R. A. Fisher, The Genetical Theory of Natural Selection (Dover [reprint], New York, 1958)
2. G. H. Hardy, Science 28, 49 (1908)
3. For a more full discussion see R. M. Anderson and R. M. May [Infectious Diseases of Humans (Oxford Univ. Press, 1991), chap. 11].
4. J. Bongaarts, Stat. Med. 8, 103 (1989)
5. R. MacArthur, Geographical Ecology (Harper & Row, New York, 1972)
Science http://www.sciencemag.org
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THEORETICAL BIOLOGY: ON BIOLOGICAL ANALYSIS
The following points are made by Eors Szathmary (Current Biology 2004 14:R145):
1) Billions of years of evolution have produced organisms of stunning diversity. Some of these are relatively simple, like the bacteria; others show impressive complexity. For two decades, the author has worked on a theoretical reconstruction and understanding of the major transitions that generated the levels of biological organization that we see today. Although many in biology have an antipathy to mathematics, the author "simply cannot live without it." A large part of his research consists of making models of intermediate stages of organization and the evolutionary transitions between them.
2) Although theoretical biology is avoided by many biologists because of their formulae phobia, theoretical biology is not necessarily mathematical, at least not when important ideas and concepts are conceived for the first time. The theory of Charles Darwin (1809-1882), as he presented it, was not mathematical (although later he commented that his reluctance to embrace mathematics was foolish, as mathematically minded persons seem to have an "extra sense"). But neither was the conceptualization by Michael Faraday (1791-1867) of the electromagnetic field: the mathematical structure was built later by James Clerk Maxwell (1831-1879). The theoretical evolutionary embryologist August Weismann (1834-1914) was often more rigorous than Darwin, but still not mathematical.
3) The Golden Age of theoretical biology was the first half of the 20th century, when Ronald Fisher (1860-1962), John Burdon Sanderson Haldane (1892-1964) and Sewall Wright (1889-1988) founded population genetics and Alfred Lotka (1880-1949), Vito Volterra (1860-1940) and Vladimir Kostitzin (1883-1963) started to build up theoretical ecology. These seeds have born many fruits since then. Take evolutionary biology, for example. A few decades after the Golden Age, evolutionary biologists started to tackle (ultimately with considerable success) questions where the Darwinian answer is far from obvious. Why do we age? Why are there sterile insect castes? At first it does not seem to make much sense to argue that your death or sterility increases your fitness. But evolutionary theory can provide satisfactory resolutions of these conundrums. In some cases even the question itself cannot be formulated well enough without some modeling: the problem of the evolutionary maintenance of sex is a case in point. Whole sub-disciplines, like evolutionary game theory, have been set up to meet such challenges.
4) The problems become a lot harder when we come to the large-scale dynamics of evolution. Imagine, say, a thousand Earth-like planets with exactly the same initial conditions of planetary development. After one, two, three billion years (and so on), how many of them would still have living creatures? And would they be like the eukaryotes? We have simply no knowledge about the time evolution of this distribution, and "educated" guesses differ widely.(1-4)
References:
1> Benner, S.A. (2003). Synthetic biology: Act natural. Nature 421, 118
2. Ganti, T. (1971). The Principle of Life (in Hungarian). (Budapest: Gondolat)
3. Ganti, T. (2003). The Principles of Life. ( Oxford University Press)
4. Maynard Smith, J. and Szathmary, E. (1995). The Major Transitions in Evolution. (Oxford: Freeman/Spektrum),
Current Biology http://www.current-biology.com
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