System identification of hunchback protein patterning in early drosophila embryogenesis

Early patterning in the Drosophila melanogaster embryo occurs through a complicated network of interactions involving transcription factor proteins and the mRNA of their target genes. One such system is the pattern of hunchback mRNA and its regulation by Bicoid and Kru¿ppel proteins. This system is well-studied, but there is disagreement amongst biologists on how exactly hunchback expression is regulated. We attempt here to provide evidence to distinguish between two models in contention, through system identification. Our general approach is to do nonlinear regression on a parametric, nonlinear partial differential equation model which incorporates transcription, diffusion, and degradation. We perform the regression, analyze the results and then interpret the results in the biological context. We also compare our results to previous work on this system.