(621g) Gap Gene Regulation In Drosophila: A Study In Multi-Objective Optimization of Spatiotemporal Models

The axial bodyplan of Drosophila melanogaster is specified during the process of embryonic morphogenesis. Maternally deposited bicoid mRNA is translated into Bicoid. This protein establishes a spatially graded morphogen distribution along the anterior-posterior (AP) axis.  Bicoid in turn triggers gap gene expression in a spatially graded manner.  The gap gene regulatory network (GRN) further refines AP patterning.  Reaction-diffusion models of gap gene expression on 1D and 3D domains have been used to infer complex GRN  interactions by optimizing model parameters with respect to gap gene expression data.  Previous studies have approached this optimization with a variety of algorithms (e.g., GA, SA), but have primarily relied on scalar cost functions (LSE, RMSE) to quantify concentration errors.  Moreover, these functions are ill-suited for identification of parameter sets which produce qualitatively correct (proper AP placement of protein bands) because they consider only quantitative agreement.  We found that the optimization problem is highly dependent on the specific choice of objective function to be minimized and that there is no clear best choice.  We evaluated spatially-extended cost functions incorporating spatial metrics (cosine similarity, spatial gradients) in 1D and 3D models.  We also decomposed the objective into concentration error and spatial contributions and explore tradeoffs in each via multi-objective optimization. To appropriately optimize spatiotemporal systems such as the gap gene network, we found that compromise between multiple objectives produced superior GRN inference.