Mathematical models of morphogen gradients and their effects on gene expression

An introduction to mathematical models of pattern formation by morphogen gradients is presented, using the early embryo of the fruit fly Drosophila as the main experimental example. Analysis of morphogen gradient formation is based on the source-diffusion-degradation models and a formalism of local accumulation times. Transcriptional control by morphogens is discussed within the framework of thermodynamic site occupancy models of gene regulatory regions. © 2012 Wiley Periodicals, Inc.