Robustness of expression pattern formation due to dynamic equilibrium in gap gene system of an early Drosophila embryo.

The first manifestation of a segmentation pattern in the early Drosophila development is the formation of expression domains of genes belonging to the gap class. In our previous research the phenomenon of the gap system's robustness, exhibited as the ability to reduce highly variable gene expression in the course of development, was explained as a result of gene cross-regulation. In this paper we formulate the rigorous robustness conditions using the inherent properties of gap gene family. We propose an approach based on the observation that for the formation of a pattern with well-established domain borders it is necessary that there exist a stationary nucleus in which the gene expression level is almost constant in time. The dynamics of gap gene expression is described by a gene circuit model that correctly reproduces the observed principles of the border positioning. We take an advantage of the fact that the system behavior in a stationary nucleus is described by an algebraic equation and hence can be easily handled analytically. This enables us to explicitly characterize the gene cross-regulation properties guaranteeing the system robustness through the spatial behavior of the patterning system along the main embryo axis. In particular, it is proved that if the total regulatory action of all the genes acting in the border formation area changes synchronously with the initial gene gradient, the system will filtrate the initial positioning error and action of highly variable external input factors. We will now show how this approach can be applied as an instrument for the analysis of the robustness mechanism and revealing new biological findings.