Pattern formation by dynamically interacting network motifs

Abstract

Systematic validation of pattern formation mechanisms revealed by molecular studies of development is essentially impossible without mathematical models. Models can provide a compact summary of a large number of experiments that led to mechanism formulation and guide future studies of pattern formation. Here, we realize this program by analyzing a mathematical model of epithelial patterning by the highly conserved EGFR and BMP signaling pathways in Drosophila oogenesis. The model accounts for the dynamic interaction of the feedforward and feedback network motifs that control the expression of Broad, a zinc finger transcription factor expressed in the cells that form the upper part of the respiratory eggshell appendages. Based on the combination of computational analysis and genetic experiments, we show that the model accounts for the key features of wild-type pattern formation, correctly predicts patterning defects in multiple mutants, and guides the identification of additional regulatory links in a complex pattern formation mechanism.

Fig. 1.

Regulatory network for Br expression in Drosophila oogenesis. (A) Schematic of a stage 10A egg chamber showing the follicular epithelium (FC), the oocyte, the stretch follicle cells (SC), and the centripetally migrating follicle cells (CMFC). Anterior (A), posterior (P), dorsal (D), and ventral (V) are shown. (B) Electron microscopy image of the wild-type Drosophila melanogaster eggshell showing the 2 dorsal respiratory appendages (DA). (Original magnification, 180×.) (C) The network diagram of br regulation by EGFR and DPP signaling pathways (see text for details). (D) Schematic representation of the dorsal views of the expression patterns of network components across 4 stages of oogenesis (stages 9–11) as observed in in situ hybridization and immunohistochemistry data (6). DPP signaling is monitored by following the spatial pattern of MAD phosphorylation (P-MAD) (6). B is reproduced from Yakoby et al. (6); C and D are modified from Yakoby et al. (6).

Fig. 2.

Model-based analysis of wild-type patterns. (A) Spatial arrangement of different cell fates (midline, roof, and lateral) in the 1-dimensional model (Left). The 1-dimensional system is shown by the black arrow. For the expression of br at stage 10B, the graph shows what the computational prediction of its concentration profile along our 1-dimensional system should look like (Right). (B) Processes included in the description of the GRK and DPP morphogens in the model. (C) Heaviside functions used to model switch-like gene regulation. (D) Simulation results for all of the network components in the wild-type background as shown by the color plots of the concentration of each component as a function of space and time. The concentrations are normalized so that their values range from 0 to 1. (E) Predicted concentration profiles of each network component in stages 9–11 of oogenesis. The colors of the graphs follow those of the expression pattern schematics shown in Fig. 1D. Numerical solution of model equations generates spatiotemporal distribution for each of the model components. The 4 chosen time points correspond to the cross-sections in the space–time plot for br expression. The 4 time points are chosen to both capture the lengths of individual stages of oogenesis and best represent the gene/protein localization data obtained from in situ hybridization and immunohistochemistry experiments.

Fig. 3.

Analysis of pattern formation in mutant backgrounds. (A) BR expression in flies with hypomorphic allele of Ras: the dorsolateral BR patches are fused into a single domain and shifted anteriorly (i and ii). TKV expression is expected to follow the BR pattern, and thus P-MAD signaling also is shifted to the anterior (iii and iv). (B) (i) In situ hybridization image of tkv in egg chambers overexpressing Mae. (iii) Immunohistochemistry experiments show that in stage 11, P-MAD is expressed in an anterior domain instead of its wild-type eyebrow-shaped pattern. Overexpression of Mae results in tkv expression that is expanded anteriorly and late P-MAD signaling that is shifted to the anterior (i–iv). (C) In an anterior clone of pnt⁻, ectopic BR expression is observed (i and ii). The clone is marked by the absence of GFP, and BR is shown in red (i). Gray box marks the location of the computationally generated pnt⁻ clone (ii). (D) Clonal analysis shows that a brk⁻ clone results in the reduction of both BR and P-MAD (i and iii). The brk⁻ clone is marked by the absence of GFP, whereas P-MAD (i) and BR (iii) are both shown in red. The model predicts that a large brk⁻ clone results in loss of P-MAD and significant reduction of BR expression (ii and iv). Arrowheads mark the dorsal midline, and dotted lines mark the perimeter of the clones; anterior is to the left. (Original magnification, 20×.)

Fig. 4.

Positive feedback loop suggested by the model. (A) In situ hybridization of tkv in CY2-DAD background shows that tkv expression is greatly reduced. (B) Simulations without the positive feedback loop predict that tkv expression in this background is indistinguishable from its wild-type expression pattern (Upper). When the positive feedback loop is included, however, simulations predict that tkv expression is greatly reduced in CY2-DAD egg chambers (Lower). (C) A positive feedback involving DPP signaling regulating the expression of its own receptor TKV is added (purple arrow) into the network presented in Fig. 1C. Here, only part of the network is shown. (D) In situ hybridization image of tkv in a CY2-DPP egg chamber. A shows dorsal view and D shows lateral view with dorsal on top; anterior to the left. Arrowheads mark the dorsal midline. (Original magnification, 20×.)