Simple rules for all walks of life

One of the great pleasures in reading a book by Ian Stewart is that you get to share in the infectious enthusiasm and sheer intellectual fun that dances through the pages. In Life's Other Secret, you also get important insights into biology from someone who sees the subject in a refreshingly different light from the narrow beams of the dominant gang of genetic reductionists. Stewart sees life whole and seeks to understand its deeper qualities using mathematics to guide both his intuition and his intellectual acumen.

The book is also a celebration of the work of a remarkable polymath, D'Arcy Wentworth Thompson, who died 50 years ago this year. Each chapter of Stewart's book starts with a quotation from Thompson's celebrated work, On Growth and Form, first published in 1917. This has now achieved cult status. Paradoxically, however, most biologists do not know quite what to make of a book of outstanding brilliance and obvious biological insight that nevertheless is highly critical of Darwinism.

Thompson was scathing about Darwin's proposed explanation of evolution in terms of genetic variation and natural selection because he believed that organisms are not arbitrary collections of adapted characters but embody deep principles of symmetry, form and transformation that limit the range of morphology and behaviour life can express. He sought a theory of life that, like physics, is explanatory of the forms assumed by matter, in this case living matter. Darwin reduced the problem of biological form to function and utility, and Thompson could not accept this elimination of organisational principles from what he saw as the order that underlies living forms.

Stewart pins his colours firmly to this mast and goes in search of these principles as they have now been revealed. He sums up the genocentric view of evolution thus: "So the flexibility of life boils down to a lot of contingency planning in its genetic code, and the complexity of life arises because the recipe for life is very, very, very, very long. You know, that's a remarkably boring explanation for such an amazing thing. Indeed, the explanation of life cannot possibly be that simple." In relation to the view that information is the key to understanding life he says: "The concept of information may be too superficial to do much more than demonstrate the existence of a problem. But if we insist on talking in such terms, then the answer seems to be this: the missing information is supplied by the mathematical rules (the laws of physics) that govern the behaviour of matter - inorganic matter - well, any matter." But this perspective is not another form of reductionism, reducing life to physics, because what is involved is new mathematics, new regularities that have been and are continually being discovered in non-living and living matter. It is the science of these emergent laws and the way genes are involved in stabilising them in living form that Stewart seeks in this book - life's other secret, not information but order.

To illustrate the general approach, the narrative starts by weaving backwards and forwards between physical forms such as snowflakes, wave patterns, vibrations and buckling patterns on spheres, compared with symmetries of leaf and flower patterns, animal coat markings, cell-cleavage patterns and gastrulation in embryos. Then it gets down to detailed expositions of various knotty biological problems and new mathematical insights into their solutions. There is the intriguing question whether the genetic code is a frozen accident, as Francis Crick believed, or if it is a necessary result of physical constraints so that if life were rerun, the same coding sequences for the amino acids would emerge. Stewart discusses this problem in relation to recent work that suggests the code itself may have evolved through a series of broken symmetries that are much more systematic than accidental, with more and more amino acids getting specified. But this is difficult territory to test empirically until we discover life on other planets. A more amenable area of study is the coiling and supercoiling of DNA. Here the topology of knots shows there is order in the twists and tangles of the big polymer, systematically described by links and writhes. Physics imposes constraints. But the problem of how proteins fold systematically into their three-dimensional shapes continues to baffle the experts. Some combination of long and short-range interactions (fields) is at work, as in a snowflake, but the precise rules remain to be discovered. Many virus coat structures, on the other hand, do conform to understood symmetry principles, as well-behaved crystals should.

There is a lot of good descriptive biology introducing each topic, from the origin of eukaryotes and cell-behaviour patterns through evolution on fitness landscapes, punctuated equilibrium and cladistics to complexity theory applied to evolution of artificial life forms and complex ecosystems. The search is always for generic or deep properties of order. The arrangement is from "simple" to "complex" in the biological hierarchy, but this does not correspond to mathematical difficulty. Some of the higher-level expressions of order receive the most elegant and economical mathematical descriptions. The trick is to spot the order, which can be very subtle. From the rich examples on offer, here is one that illustrates how simple rules, hidden in dynamic patterns, can give rise to an array of phenomena that at first appears to defy systematic explanation.

Organisms move around the world by a great diversity of methods involving different patterns of body movements. Creatures with legs have to coordinate their movements so that the body moves forwards without falling over, some legs being in the air while others are in contact with the ground to maintain balance. Not a trivial problem to solve, even though we and all tetrapods do it without thinking. Furthermore, our four-legged friends have a diversity of gaits that they use for different speeds - walking, pacing, trotting, cantering, galloping. Is there some internal logic to these patterns, or are they all just members of a continuum out of which natural selection has carved some useful modes of locomotion?

The first step is to describe the order of the patterns in terms of limb movements and then see if these are connected to one another in a systematic way. Two groups of researchers spotted relationships in terms of symmetries and broken symmetries, one of which included Stewart, whose mathematical intuition is keenly trained to recognise such properties. What is generating the order? Since limb movements involve periodic repetition of the same pattern, the obvious guess is that there are neural oscillators that fire in a particular sequence and control the limb patterns. Both groups produced solutions of the primary gaits in terms of periodic activity of these "central pattern generators" involving four interacting oscillators. But there were some problems remaining. For example, the generators did not discriminate between a pace (both left legs moving forwards together, then both right legs) and a trot, though horses certainly can, preferring to trot while camels pace.

Instead of agonising over this, Stewart and his colleague, Jim Collins, decided to have a go at movement patterns in six-legged insects. They discovered that in solving this problem they also found an elegant solution to the tetrapod patterns. By making their neural network out of six oscillators instead of four, they found a way of discriminating between a pace and a trot in terms of broken symmetries in the oscillator dynamics, and they resolved other problems such as the two types of gallops in horses, transverse and rotary. This results in some clear predictions about the activity patterns of the neural circuitry, which have still not been identified. And furthermore, this work points to deep principles of dynamic order throughout animal movement. Genes stabilise particular patterns in particular species, but it is the combination of necessary symmetries in interacting oscillators together with the physics of movement of limbs that dictates the set of possible choices for the evolution of locomotion.

This is such obvious good sense that you wonder why it is necessary to remind biologists of the importance of intrinsic principles in evolution. Maybe it is the lack of mathematics and physics in biological education that biases evolutionary thinking towards genes and information. But if we want to move forward without falling over, we need order and dynamic symmetry to keep balance. Stewart's book is a wonderfully clear and informative example of how to do this in biology.

Brian Goodwin is professor of biology and coordinator of the MSc in holistic science, Schumacher College, Devon.