A central problem in contemporary biology is to understand gene regulation in eukaryotic organisms. Increasingly abundant experimental data on both gene sequence and gene expression is providing the factual basis for progress on this problem. To unravel and fully exploit this complex data base will require more powerful ways to organize and interpret the data. The author and co-workers have developed the gene circuit method, which provides a promising approach to this problem, at the cellular level of analysis. This gene circuit method is based on three main ideas. First is the choice of protein concentrations as state variables for the description of gene regulation. Second is the summary of chemical reaction kinetics by coarse-grained rate equations for protein concentrations. Third is the use of an inverse method to determine phenomenological parameters appearing in the gene circuit in terms of expression data. Gene circuits give a systematic way to infer from gene expression data how concentrations of products of a given gene change with time and how these changes are influenced by the activating or repressing effects of other genes. A description of the gene circuit method and its application to the genetic control of pattern formation in the segmentation gene system of Drosophila will form the subject of this talk.

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1998-1999 Mathematics in Biology