Segmenting the fly embryo: a logical analysis of the pair-rule cross-regulatory module

This manuscript reports a dynamical analysis of the pair-rule cross-regulatory module controlling segmentation in Drosophila melanogaster. We propose a logical model accounting for the ability of the pair-rule module to determine the formation of alternate juxtaposed Engrailed- and Wingless-expressing cells that form the (para)segmental boundaries. This module has the intrinsic capacity to generate four distinct expression states, each characterized by the expression of a particular combination of pair-rule genes or expression mode. The selection of one of these expression modes depends on the maternal and gap inputs, but also crucially on cross-regulations among pair-rule genes. The latter are instrumental in the interpretation of the maternal-gap pre-pattern. Our logical model allows the qualitative reproduction of the patterns of pair-rule gene expressions corresponding to the wild type situation, to loss-of-function and cis-regulatory mutations, and to ectopic pair-rule expressions. Furthermore, this model provides a formal explanation for the morphogenetic role of the initial bell-shaped expression of the gene even-skipped, i.e. for the distinct effects of different levels of the Even-skipped protein on its target pair-rule genes. It also accounts for the requirement of Even-skipped for the formation of all Engrailed-stripes. Finally, it provides new insights into the roles and evolutionary origins of the apparent redundancies in the regulatory architecture of the pair-rule module.