Alan Turing’s 1952 paper on the originof biological patterning1 solved anintellectual problem that had seemed

so hopeless that it caused a great develop-mental biologist, Hans Driesch, to give upscience and turn to the philosophy of vitalism.

In the late nineteenth century, Driesch,and later Hans Spemann, demonstrated thatanimal bodies develop from a patternlesssingle cell, rather than growing from a micro-scopic, preformed version of the adult body — in humans, the ‘homunculus’. But suchself-organization, Driesch realized, could notbe understood with the ideas of that century.Before the invention of computers, appliedmathematics dealt only with linear differen-tial equations, which can amplify a patternbut not generate it.

In ‘The chemical basis of morphogenesis’,Turing showed that a pattern can indeed formde novo. In considering how an embryo’sdevelopment unfolds instant by instant fromits molecular and mechanical state, Turingwas using a modern approach. Developmen-tal biologists today similarly investigate howmolecular determinants and forces exerted by cells control embryonic patterning.

Turing’s focus was on chemical patterns: hecoined the term ‘morphogen’ as an abstrac-tion for a molecule capable of inducing tissuedifferentiation later on. This concept will befamiliar to any molecular biologist: the pro-tein products of the HOX gene cluster, forexample, which are essential for body pat-terning throughout the animal kingdom, are

morphogens in Turing’s sense. (Confusingly,the term has been more narrowly definedsince.)

At the heart of pattern-making is sym-metry-breaking. Turing considered anidealized embryo beginning with a uniformconcentration of morphogens, which havetranslational symmetry that is lost as specifictissues emerge. He raised deep questions thatare still unsolved, noting for instance that allphysical laws known at the time had mirror-image symmetry, but biological systems didnot. Turing speculated that the asymmetry of organisms originated from that of biologicalmolecules. His point is still relevant to life’sorigins.

Turing’s argument involved a mathemati-cal trick: he created a nonlinear system by turning on diffusion discontinuously in anotherwise linear system at a specific instant.Without diffusion, the system is stable andhomogeneous, but with diffusion, it becomesunstable and forms spatial pattern. The bril-liance of the trick is that the nonlinearity isconfined to a single point in time, so that atall other times, only the theory of linear equa-tions is needed. Turing cleverly arranged tohave diffusion generate pattern, rather thanblur it, as it usually does.

The influence of Turing’s paper is difficult

Pattern formationWe are only beginning to see the impact of Turing’s

influential work on morphogenesis, says John Reinitz.

to overstate. It was a transition point fromthe era of analytical mathematics to that of computational mathematics. Although hisproof was constructed analytically, Turing’spaper contains the first computer simula-tions of pattern formation in the presenceof stochastic fluctuations, and is possibly thefirst openly published case of computationalexperimentation.

Turing used analytical arguments of thenineteenth century to point the way towardsthe computational science of the twenty-firstcentury. He was well aware, however, thatnonlinear science and developmental biology would require more advanced computationalmethods. “Most of the organism, most of thetime, is developing from one pattern intoanother, rather than from homogeneity intoa pattern,” he stated1. He realized that eventhough an embracing theory for such pro-cesses might not be possible, individual casescould be modelled with a digital computer.

Yet Turing’s work is frequently misinter-preted, perhaps because he died tragically in1954, before he could correct the record. Hisanalytical arguments are often mistaken forbiological predictions, although Turing didnot intend them as such. His hypotheticalsystem, based on two substances, was a sim-plification. For the pattern-forming trick towork, one substance should catalyse synthesisof both substances while diffusing slowly; theother should catalyse destruction of both sub-stances while diffusing rapidly. For patternsthat shift over time, three substances wouldbe required. A field of investigation of thesemodels has sprung up2, but credit or blame forthe results rests with those authors, not Turing.

What Turing should receive credit for isopening the door to a new view of develop-mental biology, in which we deal directly with the chemical reactions and mechani-cal forces embryos use to self-organize theirbodies from a single cell. He was well aheadof his time. It was three decades before thework on Drosophila embryos by Lewis3,Wieschaus and Nüsslein-Volhard4 led to thediscovery of real morphogens. It is the youngresearchers of today who will benefit mostfrom reading Turing’s work — seeing his ideasabout morphogenesis not as speculation butas the conceptual framework for concreteproblems. ■

John Reinitz is in the departments of statistics, ecology and evolution, and molecular genetics and cell biology at theUniversity of Chicago, Chicago, Illinois60637, USA.reinitz@galton.uchicago.edu

1. Turing, A. M. Phil. Trans. R. Soc. Lond. B 237,37–72 (1952).

2. Kondo, S. & Miura, T. Science 329, 1616–1620(2010).

3. Lewis, E. B. Nature 276, 565–570 (1978).4. Nüsslein-Volhard, C. & Wieschaus, E. Nature 287,

795–801 (1980).

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