ACCESSION NO: 93-94-1272 TITLE: Let T Equal Tiger AUTHOR: COHEN, JACK; STEWART, IAN JOURNAL: New Scientist CITATION: November 6, 1993, 140(1898): 40-44. YEAR: 1993 PUB TYPE: Article IDENTIFIERS: TURING EQUATIONS; MORPHOGENESIS; ANIMAL DEVELOPMENT; DEVELOPMENTAL PATTERNING; MECHANO-CHEMICAL THEORY; DNA IMPRINTING ABSTRACT: Animals come in complicated shapes, which are almost always regular, not random. They can come in colors but these also form geometric patterns such as spots, stripes, or dapples. There are numerical patterns, for example the upper arm has a single bone (the humerus), two bones in the forearm, irregular rows of three followed by four in the wrist, and five fingers. Is this 1-2-3-4-5 sequence a coincidence, or do mathematical patterns lie behind the biological ones? An orthodox explanation of the form and coloring of an animal is that they are completely specified by the DNA of its genome. Various sub-sequences of DNA specify the proteins from which a tiger is made and direct them to where they are used--some proteins are pigments and make stripes--so the sequence of DNA bases in the genome might be seen as the formula for the tiger. The remarkable mathematical regularities in the form of living creatures suggests that the laws of physics and chemistry may have a major influence on the creature's form, rather than being passive carriers for genetic instructions. Shape and pattern are two forms of morphology (form in its most general sense) and the change of morphology as an organism develops is called morphogenesis. DNA is the blueprint for this. A morphogenetic equation--including some features of the organism's biology, chemistry, and physics-- is needed to describe how the physics and chemistry interact with the DNA instructions. In 1917 D'Arcy Thompson, explained the shape of a jellyfish by an analogy of gelatin falling through water--implicitly he modeled jellyfish development by the equations of fluid dynamics. He had an important point: It is not surprising that animal and plant development should follow geometric roles, since we live in a geometric universe, but does the natural geometric structure of the world have implications for morphogenesis? In 1952 the idea was picked up by Alan Turing, mathematician and computing pioneer, who argued chemical substances reacting together and diffusing through tissues could explain the formation of patterns and devised a set of "reaction-diffusion" equations to describe the distribution of chemicals in the tissue. These equations showed that patterns form spontaneously when the homogeneous (uniform) state becomes unstable, but instead of random patterning, the chemicals arrange themselves into coherent spatial patterns, called "Turing patterns." Turing saw that this type of chemical pattern in the early stages of an organism's development might act as "pre patterning," a template for further development. Chemists had trouble creating the static chemical patterns required by Turing's theories and by the 1970s, most biologists lost interest, instead concentrating on DNA code and its expression. Mathematicians, however, realized that, in Turing's "mechano- chemical" equations describing interaction of chemical changes and tissue growth, it was the common features of the whole class of equation that was important, not the specifics. This led to a general principle of pattern formation called symmetry breaking, which explains the apparent production of order from disorder. Turing's theories are coming back into vogue in a more subtle form, incorporating the reaction and diffusion of chemicals, and the responses made to them by the changes in the tissues in which they lie. So the symmetry of the developing creature changes, from the old tissue to the new. The true explanation of morphogenesis must combine the genetic switching instructions with free-running mechano- chemical dynamics. An animal can only take up a form dictated by its dynamics (the laws of physics and chemistry) and its DNA instructions, but, where several different lines of development are dynamically possible, the DNA can make the choices between them. The new mathematical models show that neither aspect alone controls development, but rather interaction of the two.