# Life's expectancy

## At Home in the Universe

This book is about the origins of life and its subsequent evolution. It is timely, given that today, seventy years after John Scopes was convicted of teaching Darwinian evolution in Dayton, Tennessee, the state legislature is considering whether to permit school boards to dismiss teachers who present Darwin's theory as a fact rather than a theory of human origin (as reported in the New York Times, March 10 1996).

Stuart Kauffmann is a highly respected theoretical biologist. His contributions to the development dynamics of fruit flies (Drosophila) are classics. Instead of describing chemical or biochemical reactions by differential equations (in which the rate of reaction is a time derivative of the concentrations of the chemical reactants as well as depending on other phenomena such as diffusion), Kauffmann applied a Boolean description - so called in honour of George Boole, one of the fathers of modern mathematical logic. The simplest example he quotes in At Home in the Universe is that of three lightbulbs 1, 2, 3, each of which receives an input from each of the other two, that is, is controlled by the other two. Each bulb can have only two states, on or off, which we can represent as 1 and 0. The idea is then to represent chemical processes by strings of 1s or 0s. Kauffmann calls these strings "Boolean networks". This formulation leads, for example, to the elegant description in Francois Jacob and Jacques Monod's classical work on cell differentiation. Genes are regarded like lightbulbs and are supposed to be on or off.

Probably the most interesting results reported in this book refer to Boolean networks characterised by two numbers: the total number of bulbs, N, and the number of inputs per bulb, K. Numerical simulations show that the number K plays an essential role. For K=N - that is, each lightbulb receives an input from all lightbulbs, including itself - we have chaotic sequences of on or off states. But for K=2, "order arises, sudden and stunning". If N=100,000, say, the system has 2100,000 states! Nevertheless, "the massive network quickly and meekly settles down and cycles among the square root of 100,000 states, a mere 317". Kauffmann successfully applies this result to living organisms, where N is then the number of genes. He shows that characteristic properties of cells, such as the cell-division cycle times, increase as approximately the square root of the number of genes. This seems to be roughly true for organisms ranging from bacteria to humans. Coincidence or not, this is an interesting result.

But the originality of Kauffman's book resides in two general claims: 1) The source of evolution is not simply Darwinian, dependent upon natural selection among random mutations. "Another source - self-organisation-is the root source of order."

2) According to this view of evolution, "this underlying order, further honed by selection, augurs a new place for us - expected, rather than vastly improbable, at home in the universe in a newly understood way."

Regarding the first point, I could not agree more. Increase of entropy was traditionally understood as an approach to disorder. Nonequilibrium thermodynamics has shown that this image is highly misleading. In far-from-equilibrium conditions new space-time structures characterised by long-range coherence may occur. Well-known examples are chemical clocks or the so-called Turing structures, structures that correspond to a new nonequilibrium crystallography. The general conditions for the appearance of these "dissipative structures" in chemistry are well known. They occur at a critical distance from equilibrium and they obey nonlinear laws of evolution, involving autocatalysis, in which some molecules play the role of both the reactant (substrate) and the product of the reaction. Life, with its interplay of nucleotides and proteins, certainly satisfies these conditions.

Moreover, I like to emphasise that near-equilibrium fluctuations are harmless, being always followed by changes that restore equilibrium; in contrast, far-from-equilibrium fluctuations may grow and lead precisely to the dissipative structures stabilised by the nonlinear processes. The new structures appear at bifurcation points corresponding to various (finite or even infinite) possibilities. The choice between these possibilities is given not by deterministic, but by probabilistic laws. So if we repeat an experiment, it may follow a different path.

Self-organisation as associated with dissipative structures has been observed at various levels of biological processes (see especially the work of Benno Hess in Germany or Brian Goodwin in Britain). The idea that life is the result of self-organisation of matter is not new (see, for example, A. Babloyantz, Molecules, Dynamics and Life, 1986). Kauffman presents a particular variant of this idea while he omits to quote his predecessors. His "central idea" is the emergence of collective autocatalysis. He writes that "when the set of model molecules reaches a critical diversity I collectively autocatalytic sets emerge I As the diversity of molecules in the model system increases, the ratio of reactions to molecules increases." In this view a critical diversity of molecules must be reached for the system to catch fire, for catalytic closure to be attained. Kauffmann argues that as the number of molecular components increases, the number of conceivable reactions increases grossly as the square of the number of molecular species and that eventually some of the many reactions will find a catalyst.

It is undoubtedly true that in many fields of science we find systems consisting of a large number of interconnected units. A striking example is the brain, where each cell has thousands of inputs from other cells. Increasing connectivity is also known to lead to bifurcation (as shown by Babloyantz). However, such systems are generally the outcome of long evolution. That they may constitute the origins of evolution is questionable.

Indeed as the number of constituents increases by a certain factor, then their concentrations decrease (approximately by the same factor) and the rate of nonlinear catalytic reactions decreases by some power of this factor. The connectivity tends to vanish. There is no discussion of this effect in Kauffmann's book. However, he is probably right when he states that life is not to be attributed to single molecules, but to bifurcations occurring in networks of catalytic reactions in accordance with the results of nonequilbrium thermodynamics mentioned above.

Kauffman applies his ideas of Boolean networks to a variety of problems. The last chapter, "An emerging global civilization", is so speculative that no serious discussion seems feasible. He introduces Boolean strings and grammars, which leads to substitutions in the strings. But no concrete example is given as to how to construct such a grammar which would mimic, say, industrial evolution. This seems to be a fantastic task. He himself writes that his grammar models are metaphors. We may leave it to economists to decide if they are useful and go to the second central theme, that we are "expected" in the universe.

To understand Kauffman's position let us turn to Monod's famous book, Chance and Necessity (1971), which Kauffman cites. Monod's conclusion was that "man knows at last that he is alone in the universe's indifferent immensity out of which he emerged only by chance". He was expressing the tragic feeling of estrangement that is part of the western intellectual heritage (and forms a major theme in the writings of Pascal or, closer to us, the historian of science, A. Koyre). More generally, in this perspective, any deterministic physicochemical interpretation of life seems doomed, as the appearance of the genetic code would have a vanishing probability at physicochemical equilibrium. Life thus looks like a kind of "miracle", considered by Monod to be a unique event.

The arrival of nonequilibrium thermodynamics and specifically the discovery of dissipative structures has altered that picture. Vortices in which billions of molecules follow each other also have a vanishing probability at equilibrium - but they are constantly produced in nonequilbrium conditions. And so we can now conceive of life as the natural outcome of classical autocatalytic processes in far-from-equilibrium situations, even if we are ignorant of the exact mechanism. In this sense we, and not only us humans, but life in general are "at home" in the universe. This is in fact a central theme in my book, Order out of Chaos (1984), written with I. Stengers.

In this sense of "at home", I therefore agree with Kauffmann. But he goes much further: not only are we "at home", he says - we are "expected". The idea returns again and again in his book as a leitmotif. I find it most unfortunate. First, if life is a result of bifurcations in nonequilibrium structures, other paths may be followed and have perhaps indeed been followed on other planets. Is our genetic code the only possible result of chemical evolution? We do not have the answer to this question. In addition what does "expected" mean here? Expected by whom? It is perhaps not a coincidence that the last page or two of Kauffman's book deals with "reinventing the sacred". Is his idea that we are "expected" not opening the way to a new, more sophisticated form of creationism? I do not know if this is his intention, but it is the reader's natural reaction.

In summary, this is an interesting book written by an outstanding biologist which explores the role of self-organisation in biological evolution, in contrast to the many current presentations based on Darwinian natural selection. It is regrettable, however, that many sections of the book are highly speculative. The future will decide if some of these sections contain the seeds of useful developments.

Ilya Prigogine, a Nobel laureate in chemistry, is director, Institutes for Physics and Chemistry founded by E. Solvay, Free University, Brussels, and director, Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin.

## At Home in the Universe: The Search for Laws of Self-Organization and Complexity

Author - Stuart Kauffman
ISBN - 0 670 84735 6
Publisher - Viking
Price - £20.00
Pages - 321

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