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

Abstract

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.

Mechanisms of scaling in pattern formation

“…These profiles are further corrected by canalization of the gap gene patterning network as it evolves to form stable patterns of gene expression (Fig. 7C) (Jaeger et al, 2007;Bergmann et al, 2007;Lott et al, 2007;Manu et al, 2009;Hengenius et al, 2011). The analysis in supplementary material Box S5 in Appendix S1 summarizes how flux optimization can lead to increases or decreases in amplitude that provide 'enough' scaling to meet the performance objectives of development in systems that do not modulate the intrinsic scale, and this may suffice for relatively small increases and decreases in length.…”

Systems biology and the integration of mechanistic explanation and mathematical explanation

“…The mathematical model of the gap gene regulatory network by Manu et al (2009aManu et al ( , 2009b) is based on and tested by data from high precision gene expression studies. It explains the robustness of gap gene pattern formation by showing that gap gene expression patterns form dynamical attractors, i.e., states toward which the system evolves and tends to return to even if temporarily removed from such an attractor state by perturbation.…”

Modelling the Bicoid gradient

“…and its protein gradient is established in less than 3 hours and is subsequently read by ~20 target genes, which are expressed in discrete patterns along the anterior-posterior (AP) axis (Jaeger et al, 2004;Schroeder et al, 2004;Ochoa-Espinosa et al, 2005;Manu et al, 2009a;Manu et al, 2009b;Ochoa-Espinosa et al, 2009).…”