Bicoid protein molecules, translated from maternally provided bicoid mRNA, establish a concentration gradient in Drosophila early embryonic development. There is experimental evidence that the synthesis and subsequent destruction of this protein is regulated at source by precise control of the stability of the maternal mRNA. Can we infer the driving function at the source from noisy observations of the spatio-temporal protein profile? We use non-parametric Gaussian process regression for modelling the propagation of Bicoid in the embryo and infer aspects of source regulation as a posterior function. With synthetic data from a 1D diffusion model with a source simulated to model mRNA stability regulation, our results establish that the Gaussian process method can accurately infer the driving function and capture the spatio-temporal dynamics of embryonic Bicoid propagation. On real data from the FlyEx database, too, the reconstructed source function is indicative of stability regulation, but is temporally smoother than what we expected, partly due to the fact that the dataset is only partially observed. To be in line with recent thinking on the subject, we also analyse this model with a spatial gradient of maternal mRNA, rather than being fixed at only the anterior pole. m.niranjan@southampton.ac.uk Supplementary data are available at Bioinformatics online.
