Simplicity To Complexity

A Mathematical Explanation For Morphogenesis


BY A. M. TURING, F.R.S. University qf Manchester

(Received 9 November 195 1 – Revised 15 March 1952)

It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biolo:~irall, unusual system. The investigation is chiefly concerned with the onset of instability. It is faund that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis.

Alan Turing’s accomplishments in computer science are well known, but lesser known is his impact on biology and chemistry. In his only published paper on biology, Turing proposed a theory of morphogenesis, the process by which identical cells differentiate, for example, into an organism with arms and legs, a head and tail.

Now, 60 years after Turing’s death, researchers from Brandeis University and the University of Pittsburgh have provided the first experimental evidence that validates Turing’s theory in cell-like structures.

The team published their findings in the Proceedings of the National Academy of Sciences on March 10.

Turing was the first to offer an explanation of morphogenesis through chemistry.  He theorized that identical biological cells differentiate and change shape through a process called intercellular reaction-diffusion. In this model, a Alan Turing system of chemicals react with each other and diffuse across a space — say between cells in an embryo. These chemical reactions need an inhibitory agent, to suppress the reaction, and an excitatory agent, to activate the reaction. This chemical reaction, diffused across an embryo, will create patterns of chemically different cells.

Imagine a field, with grass as dry as bone, teeming with grasshoppers. A small fire starts in one patch of the field and the grasshoppers hop away to avoid it. As the bugs hop, they perspire, wetting the grass along the way. The fire jumps to another part of the field, the grasshoppers hop away, creating another island of wet grass.

Now, picture an aerial view of this field — what was once a uniform plain is now spotted with patterns of burnt and unburned grass. This is Turing’s model of reaction-diffusion. The fire is the activator and the grasshoppers are the inhibitor. The reaction diffuses across a series of cells, activating some, inhibiting others and what was once identical is now different.

Turing predicted six different patterns could arise from this model.

Seth Fraden, professor of physics, and Irv Epstein, the Henry F. Fischbach Professor of Chemistry, created rings of synthetic, cell-like structures with activating and inhibiting chemical reactions to test Turing’s model. They observed all six patterns plus a seventh unpredicted by Turing.

Just as Turing theorized, the once identical structures — now chemically different — also began to change in size due to osmosis.

This research could impact not only the study of biological development, and how similar patterns emerge in nature, but materials science as well. Turing’s model could help grow soft robots with certain patterns and shapes.

More than anything, this research further validates Turing as a pioneer across many different fields, Fraden says. After cracking the German Enigma code, expediting the Allies’ victory in World War II, Turing was shamed and ostracized by the British government. He was convicted of homosexuality — a crime in 1950s England — and sentenced to chemical castration. He published “The Chemical Basis of Morphogenesis” shortly after his trial and killed himself less than two years later, in June 1954. He was just 41 years old.

Nathan Tompkins, Ning Li, Camille Girabawe from Brandeis University also contributed to this paper, along with G. Bard Ermentrout from the University of Pittsburgh.

The research was funded in part by from the National Science Foundation Material Research Science and Engineering Center grant DMR-0820492 and grant CHE-1012428.

The Belousov–Zhabotinsky Reaction is a perfect example of simple chemistry exhibiting self-organizational characteristics. Alan Turing’s “The Chemical Basis of Morphogenesis” describes how, in circular arrays of identical biological cells, diffusion can interact with chemical reactions to generate up to six periodic spatiotemporal chemical structures. Turing proposed that one of these structures, a stationary pattern with a chemically determined wavelength, is responsible for differentiation. Quantitative testing of Turing’s ideas in a cellular chemical system consisting of an emulsion of aqueous droplets containing the Belousov–Zhabotinsky oscillatory chemical reactants, dispersed in oil demonstrates that reaction-diffusion processes lead to chemical differentiation, which drives physical morphogenesis in chemical cells.

Belousov–Zhabotinsky Reaction

Computer simulation of the Belousov–Zhabotinsky reaction occurring in a Petri dish

Leave a Reply

Your email address will not be published. Required fields are marked *