  Embryonic development is driven by spatial patterns of gene expression that
determine the fate of each cell in the embryo. While gene expression is often
highly erratic, embryonic development is usually exceedingly precise. In
particular, gene expression boundaries are robust not only against intrinsic
noise from gene expression and protein diffusion, but also against
embryo-to-embryo variations in the morphogen gradients, which provide
positional information to the differentiating cells. How development is robust
against intra- and inter-embryonic variations is not understood. A common motif
in the gene regulation networks that control embryonic development is mutual
repression between pairs of genes. To assess the role of mutual repression in
the robust formation of gene expression patterns, we have performed large-scale
stochastic simulations of a minimal model of two mutually repressing gap genes
in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only
mutual repression between hb and kni, but also the stochastic and cooperative
activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the
posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni. Our
analysis reveals that mutual repression can markedly increase the steepness and
precision of the gap gene expression boundaries. In contrast to spatial
averaging and cooperative gene activation, mutual repression thus allows for
gene-expression boundaries that are both steep and precise. Moreover, mutual
repression dramatically enhances their robustness against embryo-to-embryo
variations in the morphogen levels. Finally, our simulations reveal that gap
protein diffusion plays a critical role not only in reducing the width of gap
gene expression boundaries via spatial averaging, but also in repairing
patterning errors that could arise due to the bistability induced by mutual
repression.
