From signals to patterns: space, time, and mathematics in developmental biology.

We now have a wealth of information about the molecular signals that act on cells in embryos, but how do the control systems based on these signals generate pattern and govern the timing of developmental events? Here, I discuss four examples to show how mathematical modeling and quantitative experimentation can give some useful answers. The examples concern the Bicoid gradient in the early Drosophila embryo, the dorsoventral patterning of a frog embryo by bone morphogenetic protein signals, the auxin-mediated patterning of plant meristems, and the Notch-dependent somite segmentation clock.