Morphogen gradients contribute to pattern formation by determining positional information in morphogenetic fields. Interpretation of positional information is thought to rely on direct, concentration-threshold-dependent mechanisms for establishing multiple differential domains of target gene expression. In Drosophila, maternal gradients establish the initial position of boundaries for zygotic gap gene expression, which in turn convey positional information to pair-rule and segment-polarity genes, the latter forming a segmental pre-pattern by the onset of gastrulation. Here we report, on the basis of quantitative gene expression data, substantial anterior shifts in the position of gap domains after their initial establishment. Using a data-driven mathematical modelling approach, we show that these shifts are based on a regulatory mechanism that relies on asymmetric gap-gap cross-repression and does not require the diffusion of gap proteins. Our analysis implies that the threshold-dependent interpretation of maternal morphogen concentration is not sufficient to determine shifting gap domain boundary positions, and suggests that establishing and interpreting positional information are not independent processes in the Drosophila blastoderm.

Here we characterize the expression of the full system of genes which control the segmentation morphogenetic field of Drosophila at the protein level in one dimension. The data used for this characterization are quantitative with cellular resolution in space and about 6 min in time. We present the full quantitative profiles of all 14 segmentation genes which act before the onset of gastrulation. The expression patterns of these genes are first characterized in terms of their average or typical behavior. At this level, the expression of all of the genes has been integrated into a single atlas of gene expression in which the expression levels of all genes in each cell are specified. We show that expression domains do not arise synchronously, but rather each domain has its own specific dynamics of formation. Moreover, we show that the expression domains shift position in the direction of the cephalic furrow, such that domains in the anlage of the segmented germ band shift anteriorly while those in the presumptive head shift posteriorly. The expression atlas of integrated data is very close to the expression profiles of individual embryos during the latter part of the blastoderm stage. At earlier times gap gene domains show considerable variation in amplitude, and significant positional variability. Nevertheless, an average early gap domain is close to that of a median individual. In contrast, we show that there is a diversity of developmental trajectories among pair-rule genes at a variety of levels, including the order of domain formation and positional accuracy. We further show that this variation is dynamically reduced, or canalized, over time. As the first quantitatively characterized morphogenetic field, this system and its behavior constitute an extraordinarily rich set of materials for the study of canalization and embryonic regulation at the molecular level.

Genetic studies have revealed that segment determination in Drosophila melanogaster is based on hierarchical regulatory interactions among maternal coordinate and zygotic segmentation genes. The gap gene system constitutes the most upstream zygotic layer of this regulatory hierarchy, responsible for the initial interpretation of positional information encoded by maternal gradients. We present a detailed analysis of regulatory interactions involved in gap gene regulation based on gap gene circuits, which are mathematical gene network models used to infer regulatory interactions from quantitative gene expression data. Our models reproduce gap gene expression at high accuracy and temporal resolution. Regulatory interactions found in gap gene circuits provide consistent and sufficient mechanisms for gap gene expression, which largely agree with mechanisms previously inferred from qualitative studies of mutant gene expression patterns. Our models predict activation of Kr by Cad and clarify several other regulatory interactions. Our analysis suggests a central role for repressive feedback loops between complementary gap genes. We observe that repressive interactions among overlapping gap genes show anteroposterior asymmetry with posterior dominance. Finally, our models suggest a correlation between timing of gap domain boundary formation and regulatory contributions from the terminal maternal system.

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly Drosophila melanogaster reduces over time as a result of cross regulation between these genes, a fact that we have demonstrated in an accompanying article in PLoS Biology (see Manu et al., doi:10.1371/journal.pbio.1000049). This biologically essential process is an example of the phenomenon known as canalization. It has been suggested that the developmental trajectory of a wild-type organism is inherently stable, and that canalization is a manifestation of this property. Although the role of gap genes in the canalization process was established by correctly predicting the response of the system to particular perturbations, the stability of the developmental trajectory remains to be investigated. For many years, it has been speculated that stability against perturbations during development can be described by dynamical systems having attracting sets that drive reductions of volume in phase space. In this paper, we show that both the reduction in variability of gap gene expression as well as shifts in the position of posterior gap gene domains are the result of the actions of attractors in the gap gene dynamical system. Two biologically distinct dynamical regions exist in the early embryo, separated by a bifurcation at 53% egg length. In the anterior region, reduction in variation occurs because of stability induced by point attractors, while in the posterior, the stability of the developmental trajectory arises from a one-dimensional attracting manifold. This manifold also controls a previously characterized anterior shift of posterior region gap domains. Our analysis shows that the complex phenomena of canalization and pattern formation in the Drosophila blastoderm can be understood in terms of the qualitative features of the dynamical system. The result confirms the idea that attractors are important for developmental stability and shows a richer variety of dynamical attractors in developmental systems than has been previously recognized.