Modelling the activity of the Ultrabithorax parasegment-specific regulatory domains around their anterior boundaries

The Drosophila Ultrabithorax (Ubx) gene was one of the first homeotic genes to be characterised and it specifies the phenotypic characteristics of parasegments 5 and 6. The intricate pattern of Ubx expression in these parasegments is conferred by enormous regulatory regions which, together with the structural gene, constitute the Ubx domain. A genetic, "open-for-business", model based on classical mutational analysis proposed that the regulatory regions were in fact composite structures, consisting of parasegment-specific regulatory domains that contain arrays of cell-specific enhancers which drive the intricate pattern of Ubx expression. Here, we propose a molecular mechanism, based on a survey of numerous transgenic studies, of the setting up of these parasegment-specific regulatory domains in the appropriate parts of the late blastoderm embryo. We construct a mathematical model of this mechanism using the molecular characteristics of a single initiator element, the distributions of segmentation gene products and simple competitive binding equations. We attempt to fit this mathematical model to the idealised patterns of activity and closure of the parasegment-specific domains derived from the genetic model. The resulting fitted pattern of activity and closure obtained with the simplest version of our competitive binding model shows some deviations from the idealised pattern based on the genetic model. Comparison of the predictions with recent experimental evidence suggests that the competitive binding model more accurately reflects certain features of the Ubx expression pattern--features not predicted by the genetic model.