Spatial pattern formation in biology: I. Dermal wound healing. II. Bacterial patterns

Although the development of spatial pattern and form is a central issue in biology the mechanisms which generate them are generally unknown. The interdisciplinary modelling challenge is to construct realistic mechanisms which capture the key biological processes and show how they are orchestrated to create the observed pattern. We discuss two specific patterning problems of current widespread interest in biomedicine. In the first, possible mechanisms of dermal wound healing are reviewed 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 bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data. The results from the model compare well with experiment. Mathematically, the class of models discussed 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.