Abstract
The axial bodyplan of Drosophila melanogaster is determined during a process called morphogenesis. Shortly after fertilization, maternal bicoid mRNA is translated into Bicoid (Bcd). This protein establishes a spatially graded morphogen distribution along the anterior-posterior (AP) axis of the embryo. Bcd initiates AP axis determination by triggering expression of gap genes that subsequently regulate each other's expression to form a precisely controlled spatial distribution of gene products. Reaction-diffusion models of gap gene expression on a 1D domain have previously been used to infer complex genetic regulatory network (GRN) interactions by optimizing model parameters with respect to 1D gap gene expression data. Here we construct a finite element reaction-diffusion model with a realistic 3D geometry fit to full 3D gap gene expression data. Though gap gene products exhibit dorsal-ventral asymmetries, we discover that previously inferred gap GRNs yield qualitatively correct AP distributions on the 3D domain only when DV-symmetric initial conditions are employed. Model patterning loses qualitative agreement with experimental data when we incorporate a realistic DV-asymmetric distribution of Bcd. Further, we find that geometry alone is insufficient to account for DV-asymmetries in the final gap gene distribution. Additional GRN optimization confirms that the 3D model remains sensitive to GRN parameter perturbations. Finally, we find that incorporation of 3D data in simulation and optimization does not constrain the search space or improve optimization results.
Highlights
Embryonic development in Drosophila melanogaster is initiated with the formation of spatial morphogen distributions in the early embryo
We extend the 1D model partial differential equation (PDE) to the full 3D embryonic geometry described by Fowlkes et al and compare genetic regulatory network (GRN) inferred from 1D and 3D models
In addition to GRN sensitivities highlighted by previous 1D analyses [14,38,39,44,50], we find that the 3D model exhibits fragility with respect to the shape of maternal gradients: GRNs which were inferred by optimization of 1D models showed similar gap gene patterning when applied to 3D models with DVsymmetric Bcd
Summary
Embryonic development in Drosophila melanogaster is initiated with the formation of spatial morphogen distributions in the early embryo. AP patterning events begin approximately one hour post-fertilization This patterning foreshadows the subsequent segmentation of the embryo [1,2,6,7,8,9]. Due in part to a cytoplasmic viscosity gradient common to insect embryos [10], morphogens (here, gap gene products) are thought to diffuse freely through periplasm near the embryonic surface and less substantially through the interior. They regulate transcription within the periplasmic nuclei [2]. The gap genes, in turn, regulate the pair-rule genes which in turn control segment-polarity genes and embryonic segmentation [1,2,6,15]
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