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.