Biomathematical analysis of cell invasion: migration of neural crest cells to form the enteric nervous system

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Extending scientific studies to a mathematical level is the way to produce deep understanding and control. Mathematics has been applied less to biology, particularly the biology of development, than to other branches of science, no doubt due to the innate complexity and technical difficulties of seeing and measuring what is actually going on. Labelling, imaging and computational tools to visualise biological processes are only now becoming available. To build our bodies during embryonic development, cells must move; this is called cell migration. The same process occurs throughout life in wound repair. Uncontrolled migration is the hallmark of malignant cancers, where it is called invasion. The molecular mechanisms in cells that allow them to move are just beginning to be understood. However, the big questions determining the general rules of migration are more difficult to approach. Here are some examples of such questions. When to migrate? Where to migrate to? Which pathways? How many cells to migrate? How far? How fast? How to stop? Such simple questions are still unanswered. We are pioneering a novel and unique approach combining imaging of real cells migrating in real tissues (digital time-lapse movies) with mathematical modelling to understand the driving forces of cell migration-invasion. This technology is here applied to a particular example of cell migration where precursor nerve cells migrate all the way along the length of the gastro-intestinal tract in early development. This process gives rise to fatal birth defects associated with migration failure. The development of the nervous system in the gut has features in common with all other migrations and invasions, normal and pathological. A much more profound knowledge of the big picture of the developmentally and clinically crucial process of cell migration-invasion will emerge from this marriage of biological experimentation and mathematical modelling.