270 activates or represses gene b, respectively. The quantity of Tab defines the strength of the interaction; if it is zero, the two genes do not interact. The main point of the approach is that no a priori assumptions are made about the numerical values for the elements of the matrix or the diffusion and decay rate of the transcription factors. Instead, prior to modelling, a set of quantitative expression data is collected. In this particular case, antibodies were produced against most segmentation genes, allowing the measure- ment of the protein distribution in the entire embryo at different time points. The resulting highly accurate quantitative descriptions of the spatiotemporal expression changes were used to determine the numerical values of the matrix elements and the diffusion and decay rates of the transcription factors by procedures of non-linear fitting. Thus, the network topology was recovered from experimental data, rather than being implemented prior to the actual modelling work. Initially, this approach encountered doubts and scepti- cism from molecular biologists studying the transcriptional regulation of individual segmentation genes. The analysis of cis-regulatory elements should uncover those interac- tions which actually occur in the embryo. Why would one need a more global indirect approach? However, even early gene circuit modelling using still limited experimental data sets for fitting led to some highly non-trivial predictions. For example, a paper on the formation of pair-rule gene expression stripes predicted that stripe formation requires very low diffusion rates of the pair-rule gene products (Reinitz and Sharp 1995). This prediction later gained experimental support by the demonstration that the mRNA of pair-rule genes is tightly localised to the cell cortex above the nuclei. Translation of the localised mRNA at the cortical positions is likely to hinder the spreading of the protein to neighbouring nuclei, accounting for low diffusion rates. More importantly, later modelling of the gap gene network using improved data sets for fitting and more sophisticated optimisation programmes led to results not predicted by any experimental work and in addition, provided a deeper understanding of one of the central questions in developmental biology: how spatial precision emerges despite noisy starting conditions. A careful analysis of the gap gene expression pattern showed that the gap gene domains undergo a coordinated anterior shift after their initial establishment under the control of maternal gradients (Jaeger et al. 2004b). This had not been noticed by experimentalists and implies that the readout of morphogen gradients, at least in this particular case, is not a static but rather a dynamic process. The positions of target gene domains are not ultimately fixed by particular morphogen concentrations. Rather, interactions among the target genes define the final coordinates of target gene expression. The data-fitting algorithms revealed the Dev Genes Evol (2011) 221:255–279 regulatory parameters responsible for the domain shifts and allowed an interpretation of the underlying mechanism (Jaeger et al. 2004a). The elaborate picture of the gap gene network which emerged from these studies was later expanded and used to address the problem of canalisation. The term canalisation was introduced by Waddington who pointed out ‘…that developmental reactions, as they occur in organisms submitted to natural selection are in general canalised. That is to say, they are adjusted so as to bring about one definite end-result regardless of minor variations in conditions during the course of the reaction’ (Waddington 1942). The segmentation cascade of Drosoph- ila allows one to detect canalisation at the molecular level and to analyse its mechanism. The crucial maternal morphogen responsible for activating the gap genes is the gradient of the transcription factor Bicoid. Careful measure- ments were used to detect the embryo-to-embryo variability of the Bicoid gradient and of the early and the late gap domains. A comparison of the results revealed a progres- sive reduction of the variation with developmental time. The shape of the Bicoid gradient as well as the early expression domains of the gap genes were noisier than the late gap domains. By applying the gene circuit modelling approach, the specific regulatory interactions could be identified which are responsible for the noise reduction (Manu et al. 2009a). A combination of strong and weak mutual inhibition was shown to be crucial. The mathemat- ical analysis of a precise dynamical model which contained the experimentally derived parameters revealed that the gap gene network possesses certain attractors to which the system trajectories converge, irrespective of small varia- tions in the starting conditions (Manu et al. 2009b). Thus, in this particular case, a mathematical explanation of the stability, i.e. reproducibility of an actual developmental process was achieved. The fact that modelling in this case was an a posteriori analysis of interactions occurring in the embryo is a distinctive feature of this work. The stability of steady state solutions in the face of variable starting conditions had always been a strong motive in pattern formation theory. Turing already being aware of this fact, states in the context of introducing the idea of symmetry breaking: ‘The variety of such new equilibria will normally not be so great as the variety of irregularities giving rise to them’ (Turing 1952). Gierer and Meinhardt also considered the stability of the outcome of pattern formation processes in spite of system perturbations as one of the most essential aspects of their theory (Gierer 1981; Meinhardt 1982). However, the papers on the gap gene network represent probably the first case in which quantitative data, including an assessment of the actual noisiness of the system have been used as the basis for modelling. Despite these seminal achievements and the obvious closeness to biological reality, the gene circuit approach