Introduction Traditional view of pattern formation in the early Drosophila embryo is essentially one-dimensional: The anterior, posterior, and terminal systems initiate the formation of bands and stripes of gene expression along the AP axis; at the same time, the orthogonal gradient of Dorsal (Dl) controls a different set of genes along the DV axis. These maternal patterning signals were believed to act independently from one another until they integrate at the enhancer of their zygotic target genes . Recently, we have shown that in addition to this widely accepted idea of a genetic developmental program, the maternal signals can integrate upstream of the zygotic gene regulation through a substrate competition mechanism . Specifically, the anterior morphogen Bicoid (Bcd) interacts with the terminal system and acts as a competitive inhibitor of the terminal signaling. In the early embryo, the terminal patterning is mediated by localized activation of Mitogen Activated Protein Kinase/Extracellular Regulated Kinase (MAPK/ERK). MAPK functions downstream of Torso, a uniformly expressed receptor tyrosine kinase that is presented with its ligand at the anterior and posterior poles of the embryo. Spatially restricted Torso signaling regulates the expression of genes required for the development of the terminal structures such as tailless and huckebein. This depends on MAPK-mediated phosphorylation of transcriptional repressors Capicua (Cic) and Groucho (Gro), both of which are uniformly distributed throughout the embryo . In the anterior region, Bcd competes with Cic and Gro and other MAPK substrates to bind to the activated MAPK (dpERK), lowering MAPK mediated downregulation of these repressors. As a consequence, the level of Cic is significantly higher in the anterior region compared to the posterior . However, the functional significance of this asymmetric MAPK signaling at the termini remains unclear. Using a biophysical model and genetic experiments, we propose that this observed asymmetry of MAPK signaling is functionally significant and can explain genes that exhibit both AP and DV polarity. Specifically, we suggest that wild type expression of zerkt (zen) requires this differential signaling gradient of the terminal system. Our work suggests an additional layer of integration of AP and DV signaling systems and provides a plausible mechanism for regulation of 2-dimensional gene expression patterns in the embryo. Results and Discussion Our mathematical model is based on the quantitative experimental information about Bcd, Dl, and terminal gradients, and biophysical descriptions of reaction and diffusion in the syncytial blastoderm. Since Dl gradient acts perpendicular to Bcd and dpERK, the embryo needs to be modeled as a 2-D system. Although the real embryo looks like an ellipsoid, for illustrative purposes, we considered a rectangular embryo where the x and y directions represent AP and DV axes of the real embryo respectively. We assumed that the AP and DV systems do not interact until they integrate at the DNA to regulate their common target gene such as zen: Hence the two axes are treated as two independent systems. Our model analyzes the regulatory interactions of zen described previously . Briefly, zen is activated by a spatially uniform activator (X), but is repressed by Dl and repressor complex (Dl-R) . Since zen repression requires both Dl and R, we model their joint action by the product of their concentrations. At the poles, dpERK antagonizes Dl mediated repression as it deactivates Dl corepressor through phosphorylation. In the anterior region, Bcd presents as an extra substrate of dpERK that can compete with R. Bcd gradient is modeled as an exponentially decaying curve with maximum at the anterior tip (x=0). The competition between Bcd and the R acts as if Bcd is an indirect inhibitor of dpERK mediated phosphorylation of R. We use the switch-like model of gene regulation, where zen is only expressed when the product Dl and R is below some constant threshold, To. Thus, the level of zen expression is given by zen(x,y) = H(To-R(x)*Dl(y)), where H(u) is the Heaviside step function: H(u) = 1, when u>0 and 0 otherwise. The spatial pattern of the repressor, R(x), is found from a reaction-diffusion problem that describes the MAPK-mediated phosphorylation of the repressors. We assume that the MAPK kinase (A), its phosphatase (D), and Bcd are in excess; hence, their concentrations profiles are parameters/inputs and not variables of the model. The spatial pattern of MAPK kinase, A(x) activity has peaks at both the anterior and the posterior poles. We neglect the dephosphorylation of MAPK substrates, and assume that all species have the same diffusivity and all substrates are phosphorylated with the same kinetics. Under these assumptions, the model has 6 variables: unphosphorylated repressor (R), inactive and active MAPK (E and E*), and active MAPK in complex with Bcd, R, or MAPK phosphatase (BE*, RE*, and DE*, respectively). The model predicts that the level of R is higher at the anterior than the posterior pole. This reflects the effect of substrate competition since Bcd is distributed in the AP gradient and thus, competes with the repressor for binding to phosphorylated MAPK only in the anterior region, resulting in an AP asymmetric pattern of R. A level set (line of constant value) of the product of the Dl and R patterns, Dl(y)*R(x), gives the 2D boundary of the zen pattern. Our model can predict how this pattern changes in response to variations in the levels of anterior, terminal, and DV signals. For instance, the model correctly predicts that the ectopic expression of zen in embryos that lack Dl. In addition, the terminal signaling has much stronger effect on antagonizing Dl mediated repression at the posterior pole. With regard to the asymmetric pattern of zen, our model predicts that lowering the dose of Bcd should lead to ectopic zen at the anterior since MAPK signaling activity toward the uniform repressor is increased in the absence of its competing substrate, Bcd. To test this prediction, we examined zen expression in embryos derived from bcd mothers. We found that zen is no longer repressed in the anterior region in these embryos. In the absence of Bcd, zen is expressed all around anterior pole and shows nearly symmetric pattern at both poles. This expansion most likely reflects increase level of MAPK signaling in these embryos since Dl gradient is not significantly affected in these embryos, and zen is expressed in the anterior region despite the high level of nuclear Dl. In the wild type embryos, anterior zen is expressed only to the point where Dl level becomes very low, whereas at the posterior pole, zen and Dl are co-expressed. However, in the embryos lacking Bcd, zen and Dl are co-expressed not only at the posterior, but also at the anterior pole. Conclusion We have developed a network type interaction model for regulation of zen. Specifically, we have focused on the AP asymmetry of zen expression, reflecting differential modulation by the terminal signaling at the poles. Based on the biophysical model, we argue that zen is repressed in the anterior region due to stronger MAPK substrate competition induced by Bcd. Our results provide new insights to coupling of different signaling systems in patterning of the early embryo. We have established that MAPK can integrate inputs from other maternal morphogens such as Bcd via substrate competition. Through a biophysical model and genetic experiments, we showed that this new mechanism of signal integration is functionally significant; it is required for patterning of zen. In the future, our model can be extended to examine the joint effects of anterior, terminal, and dorsoventral signaling systems in patterning of the embryo. References  Papatsenko, D., Goltsev, Y., and Levine, M. (2009) Organization of developmental enhancers in the Drosophila embryo. Nucleic Acid Research 37, 5665-5667.  Kim, Y., Coppey, M., Grossman, R., Ajuria L, Jimenez, G., Paroush, Z., and Shvartsman, SY. (2010). MAPK substrate competition integrates patterning signals in the Drosophila embryo. Current Biology. 20, 446-451.  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