Chemical and Biological Applications of Turing Systems

Abstract

Turing’s paper on diffusion-driven instabilities in nonequilibrium reaction–diffusion systems as a means of biological pattern formation [440] attracted little attention for about two decades, as shown by the citation histogram in Fig. 12.1. One of the first scientists to be intrigued by Turing’s ideas was Wardlaw, a botanist who thought about ways to test the mechanism experimentally [468, 470, 469]. By the early 1970s theoretical biologists and biomathematicians began to explore in earnest if Turing instabilities could explain spatial pattern formation in a variety of living systems and a considerable body of theoretical work was produced, see for example [157, 279, 231, 239, 182, 183, 264, 261, 308]. Morphogen-based pattern formation, where the long-range influence of signaling molecules induces structure, is a well-established phenomenon in developmental biology [26]. However, definitive evidence for a Turing mechanism of pattern formation within a morphogen system is still lacking. Several promising candidate systems exist and are discussed in Sect. 12.2.