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  • Print publication year: 2016
  • Online publication date: March 2016

9 - Turing's Theory of Developmental Pattern Formation

from Part Three - The Reverse Engineering Road to Computing Life
    • By Philip K. Maini, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Thomas E. Woolley, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Eamonn A. Gaffney, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Ruth E. Baker, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
  • Edited by S. Barry Cooper, University of Leeds, Andrew Hodges, University of Oxford
  • Publisher: Cambridge University Press
  • DOI: https://doi.org/10.1017/CBO9780511863196.014
  • pp 131-143

Summary

Introduction

Elucidating the mechanisms underlying the formation of structure and form is one of the great challenges in developmental biology. From an initial, seemingly spatially uniform mass of cells, emerge the spectacular patterns that characterise the animal kingdom – butterfly wing patterns, animal coat markings, skeletal structures, skin organs, horns etc. (Figure 9.1). Although genes obviously play a key role, the study of genetics alone does not tell us why certain genes are switched on or off in specific places and how the properties they impart to cells result in the highly coordinated emergence of pattern and form. Modern genomics has revealed remarkable molecular similarity among different animal species. Specifically, biological diversity typically emerges from differences in regulatory DNA rather than detailed protein coding sequences. This implicit universality highlights that many aspects of animal development can be understood from studies of exemplar species such as fruit flies and zebrafish while also motivating theoretical studies to explore and understand the underlying common mechanisms beyond a simply descriptive level.

However, when Alan Turing wrote his seminal paper, ‘The chemical basis of morphogenesis’ (Turing, 1952), such observations were many decades away. At that time biology was following a very traditional classification route of list-making activities. Indeed, there was very little theory regarding development other than D'Arcy Thompson's classic 1917 work (see Thompson, 1992, for the abridged version) exploring how biological forms arose, though even this was still very much at the descriptive rather than the mechanistic level.

Undeterred, Turing started exploring the question of how developmental systems might undertake symmetry-breaking and thus create and amplify structure from seeming uniformity. For example, if one looks at a cross-section of a tree trunk, it has circular symmetry which is broken when a branch starts to grow outwards. Turing proposed an underlying mechanism explaining how asymmetric structure could emerge dynamically, without innate hardwiring. In particular, he described how a symmetric pattern, for instance of a growth hormone, could break up so that more hormone was concentrated on one part of the circle, thus inducing extra growth there.

In order to achieve such behaviour Turing came up with a truly ingenious theory. He considered a system of chemicals reacting with each other and assumed that in the well-mixed case (no spatial heterogeneities) this system exhibited an equilibrium (steady) state which was stable.

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