Dev Genes Evol (2011) 221:255–279 remains at the phenomenological level in one basic respect. The elements of the interconnectivity matrix are open to a number of molecular interpretations and they are also not free from a priori assumptions which might not fully reflect the complexity of the transcriptional process. For example, the model does not allow that a transcription factor activates and represses at low or high concentrations, respectively. Exactly this situation has been discussed for one of the key gap genes, hunchback, with regard to its regulation of Krüppel (Papatsenko and Levine 2008). The fact that the authors can produce a self-consistent model for the gap gene network without assuming more complex interactions may have three explanations. (1) These more complex interactions might in fact not exist and the experimental evidence provided by molecular biologists is based on artefacts. (2) The interactions exist, but are not relevant for the dynamics. (3) The derived network, in spite of recovering the quantitative dynamics of the system, is only a partial approximation of the reality and might even wrongly suggest interactions which have no molecular counterpart in the embryo. A crucial question will be how the model fares when applied to the next level of the segmentation process: the emergence of the pair-rule gene expression pattern. At this level, several fundamental questions still need to be addressed, in particular the precise phase shift between partially overlapping pair-rule stripe patterns. This phase shift is crucial for initiating segment formation (Klingler and Gergen 1993; Warrior and Levine 1990), but we are almost completely ignorant with regard to the underlying molecular mechanisms. Here, the gene circuit model might indicate where to look at the molecular level, and thus could have a crucial heuristic role for the working molecular biologist. On the other hand, there is some indication that besides protein–DNA interactions, protein– protein interactions between the pair-rule gene transcription factors also contribute to the patterning process (Fitzpatrick et al. 1992). Such interactions have not been included in the gene circuit model equation to date, and it is doubtful whether they can be fully represented. Any mechanism which necessitates the elements of the interconnectivity matrix to become functions of space and time will probably render the optimisation problem unsolvable. Thus, it is possible that the gene circuit model in its current form has a very limited applicability. There might be few other instances in all developmental biology, which suit this approach as much as the first step in the Drosophila segmentation cascade, the gap gene network. (3) The last example deals with a question which for a long time was assumed to be trivial and did not require particular modelling efforts: the formation of a simple morphogen gradient from a localised source. Crick (1970) had already provided a special solution to this problem. The 271 particular case in question is the aforementioned gradient of the transcription factor Bicoid, which provides the input for the gap gene pattern (Porcher and Dostatni 2010; Grimm et al. 2010). Bicoid mRNA is localised to the anterior pole of the egg where it is translated generating a local source of Bicoid protein which diffuses to more posterior regions of the embryo (Driever and Nüsslein-Volhard 1988a, b). Even intuitively, one can imagine how local production and diffusion are able to produce a long-range concentration gradient. This intuitive concept can be captured in a simple equation describing the spatiotemporal change of Bicoid concentration as a function of synthesis, decay and diffusion (SDD model). For SDD models, steady-state distributions can be calculated in which synthesis, diffusion and decay are balanced such that the resulting concentration profiles do not change in time (Gregor et al. 2005). A localised source and spatially uniform decay give rise to an exponential steady-state profile characterised by a length scale which only depends on the diffusion and decay rates. Measurements of the Bicoid gradient indeed showed an exponentially decaying concentration profile which was sufficiently stable for assuming a steady state (Driever and Nüsslein-Volhard 1988b; Gregor et al. 2005). Furthermore, measurements of the diffusion of fluorescent dextran molecules which had a molecular mass comparable to that of Bicoid were in agreement with the SDD model for gradient formation (Gregor et al. 2005). However, one phenomenon suggested a more complex scenario. Closely related fly species show almost identical early segmentation gene expression. However, their egg size may vary over more than a factor of five in length (Gregor, et al. 2005). The scaling of the segmentation gene expression pattern can be traced back to the scaling of the Bicoid gradient, i.e. the gradients from different flies have the same relative concentration profiles irrespective of the egg size. Thus, in a large egg, the gradient has a proportionally larger length scale which might result either from an increased diffusion or a decreased decay rate of Bicoid protein. However, the Bicoid proteins of different fly species have a very similar structure and thus should have similar diffusion and decay rates implying similar length scales. This assumption was strongly corroborated by generating Drosophila melanogaster embryos express- ing a Bicoid protein derived from a fly species with large eggs (Gregor et al. 2008). The heterologous Bicoid protein formed a gradient indistinguishable from the endogenous one. Thus, scaling seems to be a feature of the embryonic system rather than of the respective Bicoid protein. To explain this fact, a cellular property had to be found which also showed scaling behaviour. An obvious candidate was the number of nuclei, which is conserved in different fly species. Flies with large eggs have a lower nuclear density, and those with small eggs a higher one. As a transcription