Murray 2000

James D. MURRAY

Pattern formation in integrative biology – a marriage of theory and experiment — (CRAS 323 (2000) 1:1-144)

            The art of good modelling in biology relies not only on sufficient mathematical expertise (often not at all sophisticated), but also on : a) a sound understanding and appreciation of the biological problem; b) a realistic math representation of the important biological phenomena; and c) a biological interpretation of the mathematical analysis and results in terms of insights and predictions. Mathematical or theoretical biology to be scientifically relevant is unquestionably an interdisciplinary science par excellence.

            Pattern formation studies are sometimes criticised for their lack of inclusion of genes in the models. But then criticism can be levelled at any modelling abstraction of a complex system to a relatively simple one. It should be remembered that the generation of pattern and form, particularly in development, is usually a long way from the level of the genome. Of course genes play crucial roles in development but they do not actually create patterns. Many of the evolving patterns could hardly have been anticipated solely by genetic information.

            We suggest that math modelling must be used if we ever hope to genuinely and realistically convert an understanding of the underlying mechanisms into a predictive science. Mathematics is required to bridge the gap between the level on which most of our knowledge is accumulating (cellular and below) and the macroscopic level of the patterns we see. A math approach lets us explore the logic of pattern formation.