Bones, feathers, teeth and coat markings: a unified model.
A first necessary criterion to be met by any model for pattern formation is that it must be able to reproduce the patterns it purports to model. The above examples show how simple ideas from self-organisation can produce spatial patterns of varying complexity that are consistent with those observed experimentally. Second, the model must be consistent with the results of experimental manipulation. Third, the model must make experimentally testable predictions. In this way, a mathematical model can help to elucidate the underlying biochemical and biophysical mechanisms of pattern formation. I have tried to illustrate these ideas with the above examples. These examples also show the breadth of patterning phenomena that can be captured by these models. In animal coat markings, the patterns are laid down simultaneously. In limb development, the skeletal elements are laid down sequentially. The application to feather germ formation illustrates complex sequential regular pattern formation, while the application to tooth primordium formation illustrates sequential irregular pattern formation. Many other patterning phenomena have been studied (see, for example, ref. 7). Pattern formation is one of the central issues in developmental biology and intense interdisciplinary research involving experimentalists and theoreticians is beginning to help us understand how this phenomenon occurs. A detailed understanding of normal development is a necessary first step to the understanding of abnormal development and, hopefully, will help medical science combat developmental defects.