SPATIAL PATTERN-FORMATION IN BIOLOGY - I - DERMAL WOUND-HEALING - II - BACTERIAL PATTERNS

Although the development of spatial pattern and form is a central issu e in biology the mechanisms which generate them are generally unknown. The interdisciplinary modelling challenge is to construct realistic m echanisms which capture the key biological processes and show how they are orchestrated to create the observed pattern. We discuss two speci fic patterning problems of current widespread interest in biomedicine. In the first, possible mechanisms of dermal wound healing are reviewe d with a discussion of what is needed of realistic models for studying wound healing. We then list a series of open problems. In the second problem we describe a model for the complex patterns formed by bacteri al colonies, specifically Escherichia coli, and derive and analyse a m odel firmly based on experimental data. The results from the model com pare well with experiment. Mathematically, the class of models discuss ed gives rise to novel systems of partial differential equations which pose challenging problems, both analytical and numerical. The models have provided the experimentalist with insight as to how such patterns might be formed and have suggested possible experiments to elucidate the underlying biological processes. (C) 1997 The Franklin Institute. Published by Elsevier Science Ltd.