Modelling the Drosophila embryo.

I provide a historical overview on the use of mathematical models to gain insight into pattern formation during early development of the fruit fly Drosophila melanogaster. It is my intention to illustrate how the aims and methodology of modelling have changed from the early beginnings of a theoretical developmental biology in the 1960s to modern-day systems biology. I show that even early modelling attempts addressed interesting and relevant questions, which were not tractable by experimental approaches. Unfortunately, their validation was severely hampered by a lack of specificity and appropriate experimental evidence. There is a simple lesson to be learned from this: we cannot deduce general rules for pattern formation from first principles or spurious reproduction of developmental phenomena. Instead, we must infer such rules (if any) from detailed and accurate studies of specific developmental systems. To achieve this, mathematical modelling must be closely integrated with experimental approaches. I report on progress that has been made in this direction in the past few years and illustrate the kind of novel insights that can be gained from such combined approaches. These insights demonstrate the great potential (and some pitfalls) of an integrative, systems-level investigation of pattern formation.