The gene circuit method.

Top panel: a Drosophila embryo is modelled as a row of nuclei that undergo mitosis. Each nucleus contains four gap genes: hunchback (hb), Krüppel (Kr), giant (gt) and knirps (kni). The products of these genes diffuse, decay, and interact with each other to regulate gene expression. In addition gap genes are regulated by four external inputs, provided by the gene products of bicoid (bcd), caudal (cad), tailless (tll) and huckebein (hkb). Central circle: fitting the model to quantitative, spatial expression data is done via an iterative optimisation algorithm. A gene circuit with random regulatory parameters is used as the starting point for an exploration of parameter space. This is achieved by repeatedly changing parameter values to yield new gene circuit solutions. For each of these solutions model output is calculated and compared to the data by evaluating the sum of squared differences between the two. New gene circuit solutions are selected according to a global optimisation strategy (see Materials and Methods). The aim is to improve the fit to the gene expression data over many iterations until no further improvement can be achieved. Bottom panel: gene circuits that accurately reproduce expression data contain parameter estimates that encode a specific regulatory network structure. These models are analysed to yield insights into the regulatory dynamics and function of each interaction in the network.