CHAPTER 34

Turing’s theory

of morphogenesis

thomas e. woolley, ruth e. baker,

and philip k. maini

I

n 1952, Turing proposed a mathematical framework for understanding certain very

interesting chemical reaction systems.^1 He described a rather counter-intuitive chemical

mechanism, and showed that it could generate patterns in chemical concentrations. He

coined the term ‘morphogens’ for the chemicals composing his mechanism, and he hypoth-

esized that morphogens instruct cells to adopt different fates. Which future is ‘selected’ by

the cell depends on the concentrations of morphogens to which the cell is exposed. Thus a

new field of research was born, leading to novel mathematical developments and to new

biological experiments. However, researchers continue to hunt for a biological example of

Turing’s mechanism in which the morphogens can be identified. Here we briefly review sixty

years of research inspired by Turing’s seminal paper.

Introduction

This chapter is a non-mathematical introduction to the mathematical techniques that allow

us to understand the mechanisms behind the formation of biological patterns, such as the

development of stripes on the skin of a zebra. In particular, we can extract general rules from

the mathematical models, and these aid us in identifying places where such patterns could be

found. We highlight the successes of Turing’s theory, discuss its applicability to particular real-

life examples, and explain the potential solutions that it offers to problems thrown up by recent

advances in biology.

The core idea of Turing’s theory is to take two stable (or stabilizing) processes and com-

bine them. What will you get? Intuitive reasoning suggests that the outcome is a stable system.

Turing showed that this is sometimes the wrong answer.