Canalization of Gene Expression and Domain Shifts in the Drosophila Blastoderm by Dynamical Attractors

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.Author Summary: C. H. Waddington predicted in 1942 that networks of chemical reactions in embryos can counteract the effects of variable developmental conditions to produce reliable outcomes. The experimental signature of this process, called “canalization,” is the reduction of the variation of the concentrations of molecular determinants between individuals over time. Recently, Waddington's prediction was confirmed in embryos of the fruit fly Drosophila by observing the expression of a network of genes involved in generating the basic segmented body plan of this animal. Nevertheless, the details of how interactions within this genetic network reduced variation were still not understood. We use an accurate mathematical model of a part of this genetic network to demonstrate how canalization comes about. Our results show that coupled chemical reactions having multiple steady states, or attractors, can account for the reduction of variation in development. The variation reduction process can be driven not only by chemical steady states, but also by special pathways of motion through chemical concentration space to which neighboring pathways converge. These results constitute a precise mathematical characterization of a healing process in the fruit fly embryo.