Times Literary Supplement

Review of
Stuart Kauffman's
At Home in the Universe
The search for laws of self-organization and complexity
32lpp. Viking. E20.
0 670 84735 6

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We humans have lost our place in the universe to science: Copernicus booted us out of the centre of the cosmos, and Darwin knocked us off the apex of life. Here we are relegated, among the rest of known life, to a happy but highly improbable accident, occupying a smallish planet orbiting a mediocre star somewhere on the outer edge of a quite ordinary galaxy, one among many billions of such galaxies, as if we'd crashed a party where we don~t belong. Stuart Kauffman claims that we do belong, arguing that life, rather than being so improbable, is an almost inevitable consequence of the natural occurrence of spontaneous order, of self-organization. Hence the title of his book; we're At Home in the Universe.

But how so? First, consider a reaction between two chemicals being catalyzed by a third. A collection of chemicals, where each reaction between two of its number is catalyzed by another member of the same collection, is called an autocatalytic set. Kauffman argues that such autocatalytic sets are to be expected to occur via natural self-organizational processes. The argument is based on a computer model of random graphs that can be easily understood by means of a simple thought experiment.

Imagine strewing a multitude of buttons randomly about a bare floor. Now pick two buttons at random and join them by a thread. Put them back. Choose another two, connect and return them. Continue this process, keeping track of the number of buttons in the largest connected cluster, that is, the largest group of buttons that could be lifted together by picking up one of its members. Kauffman's computer models of this experiment show that this largest connected cluster grows slowly until the number of threads is a little more than half the number of buttons. Then, suddenly, it grows large very quickly. In models containing 400 buttons, this maximal cluster size goes from under 50 to over 350 as the number of threads rises from just below 200 to just above 250. Plotting a graph of maximal cluster size against number of threads yields a steep S-curve.

Kauffman likens this sudden rise in maximal cluster size to a phase transition, as when water suddenly changes to ice as the temperature drops below freezing. Here the phase transition is between chaos and order, our random graph being chaotic when it consists of lots of small unconnected clusters, and ordered when only a few large clusters exist. Such phase transitions recur in all of Kauffman's models as the book progresses.

But what has all this to do with the origin of life? To see, let us extend our thought experiment. This time, buttons will represent chemicals, reactions between them, and their products. Black threads join each of two chemicals to a button representing their reaction. Another black thread joins the reaction button to a button representing the product of the reaction. Kauffman calls the resulting graph a reaction network. Within such reaction networks, he expects to find autocatalytic sets.

Chemicals in our reaction networks can not only play the roles of reactors and reaction products, but can also serve as catalysts for other reactions. For each such catalyzed reaction, connect the catalyst button to the reaction button with a blue thread, and change the threads representing the reactions from black to red. Autocatalytic sets are now easy to recognize. All of their threads are red, and their catalysts also belong to the set.

Imagine, now, a chemical system with available basic ingredients and an outside source of energy. Kauffman asserts that beyond some level of complexity, autocatalytic sets can be expected to emerge spontaneously, much as the large maximal cluster did in our random graph. He argues that "the spontaneous emergence of self-sustaining webs is so natural and robust that it is even deeper than the specific chemistry that happens to exist on earth; it is rooted in mathematics itself".

Arguing from the expected appearance of such autocatalytic sets, Kauffman contends that life didn't evolve from self-replicating molecules, as is the common belief (see Christian de Duve's Vital Dust, 1994). Rather, he suggests, "life emerged . . . not simple, but complex and whole". By this he means that life first appeared on Earth in the form of a cellular creature not much different from pleuromona, the simplest bacterium alive today. He also concludes that life should be common throughout the universe rather than rare.

Having secured a place in the universe for bacteria, Kauffman examines human development. Consider another thought experiment: this time, strew the floor with light bulbs, including their sockets and controllers (or programmable switches). Wire them together randomly. Attach a power source and a clock. Now suppose that whether or not a bulb is lit depends on its current state and those of its neighbours. For example, one bulb's controller may be a goalong-with-the-crowd type that turns on its bulb only when a majority of the bulbs to which it is directly attached are on. Other controllers will operate on different rationales. The result will be a network of light bulbs, some lit, some off, initially at random. In this "Boolean net", each controller looks at its neighbours and calculates its next state, on or off. At the next tick of the clock, all bulbs switch to their computed new states simultaneously. The net continues to unfold in this way over time. This unfolding is referred to as its dynamics.

Suppose we take a snapshot of our light bulb network at one moment. We'll call the pattern of on and off bulbs that this snapshot portrays the configuration of the network. The configuration changes at every time tick according to the various update rules embodied in the individual controllers. Beginning with some initial configuration (which we shall call C), there will be a sequence of configurations which we can call the trajectory of C.

What must such a trajectory look like? Perhaps some configuration along the way remains unchanged at the next clock tick. If so, it must remain unchanged for each tick thereafter, so that the trajectory becomes fixed. Otherwise, since the number of bulbs is finite (and thus the number of configurations is finite), some earlier configuration, say C1, must eventually be repeated. In this case, the trajectory is then destined to repeatedly cycle through the successive configurations occurring between C1 and its reoccurrence. The shorter this cycle, the more orderly Kauffman considers the dynamics of the net; the longer, the more chaotic. If the cycle is long enough, we'll not be able to wait around to see that the net repeats itself.

In such Boolean nets, trajectories of many different initial configurations may lead into the same cycle. The cycle then represents an "attractor" of the system, and the collection of initial configurations whose trajectories eventually fall into the cycle is called the basin of that attractor. An ordered Boolean net is one with few attractors, each with a large basin and a short cycle. A chaotic system will have very many chaotic (long-cycle) attractors each with a small basin.

For decades, Stuart Kauffman has experimented with computer models of Boolean nets, looking for parameters that produce either order or chaos. One such is the density of connections. The more wires into a bulb, the more chaotic the system; the fewer, the more orderly. Another such parameter is the ratio of the number of situations in which a bulb turns on to the number in which it turns off. At some critical value of this parameter, even a densely connected net swings from chaotic to ordered. The upshot of all this is that mathematical properties of Boolean nets determine order or chaos.

Having produced these Boolean nets, Kauffman proceeds to specialize them so as to argue for the appearance of spontaneous order in evolution, in ontogeny, in technology, in organizations. He gives us a spectacular view; let's start with his perspective on evolution.

Particular genes contribute to the fitness of their organism. For example, the genes that result in a large, thick, dark mane enhance the fitness of a lion who must, on occasion, fight another lion for possession of a pride of lionesses. The mane is part bluff, giving the appearance of larger size, and part protection for the vulnerable neck. But genes don't typically work alone. Their fitness contribution is affected, in complex ways, by the actions of other genes. In the case of the mane, genes for long canines
and sharp claws play a supporting role. Geneticists refer to this phenomenon as epistatic coupling.

Kauffman builds Boolean nets whose bulbs represent genes and whose connecting wires represent epistatic couplings. Each bulb makes a fitness contribution which depends on its own state of illumination and those of its neighbours. Kauffman takes the average of these fitness contributions as the overall fitness of the genome, as represented by the configuration of the net. The space of all such configurations, together with their associated fitnesses, constitute the fitness landscape associated with that species. Evolution is seen as a hill-climbing search through this fitness landscape, looking for higher fitness.

Certain values of the parameters of these nets lead to rugged fitness landscapes with very many low peaks where it would be impossible for complex organisms to evolve. Tuning these parameters can result in smooth landscapes where a high fitness is easier to find. Experimenting with these models leads Kauffman to believe that by tuning epistatic coupling of genes, natural selection tunes landscapes from rugged to smooth, allowing the evolution of complex organisms. Thus, natural selection builds on underlying spontaneous self- organization to produce evolution.

Looking in another direction from our Boolean net vantage point, we find the issue of cell differentiation, a part of ontogeny. How is it that more than 200 types of cells, as different as neurons and muscle cells, develop in the human body, all with identical genomes? What makes one cell develop into a neuron while another, with identical genome, opts for becoming a muscle cell? The answer seems to lie with one gene's ability to turn another on or off. Though the genomes are identical in the muscle cells and neurons of an individual organism, the sets of active genes are not. Therein lies the difference.

Let's build a Boolean net modelling a genetic regulatory system inside a cell. Here, bulbs represent genes and their products all interacting with each other in marvelously complex ways, and turning one another on and off. How does the cell decide to become a neuron, say? The trajectory of our Boolean net model of the cell falls into the basin of some attractor. Kauffman suggests that this attractor, a sequence of configurations of the model, determines the cell type.

Next, we turn toward technology and the evolution of artefacts. A new invention, say the bicycle, evolves rapidly through the natural selection of the marketplace into a multitude of forms. I recently saw an exhibition of early bicycles that contained models with one large wheel and one small, some with the large in front, some with the small, and with different seat placements and different drive mechanisms. There was more diversity than I could ever have imagined. Kauffman notes that it is typical "to find a wide range of dramatic early experimentation with radically different forms, which . . . then settle down to a few dominant lineages". Once again he constructs Boolean net models that predict observed features of product evolution.

Such models also shed light on the evolution of organizations and on extinctions, both of species and of artefacts (steam locomotives, or the endangered typewriter). Kauffman's arguments in this area are insightful and convincing, and worth attending to in their full detail.