Latent force models for describing transcriptional regulation processes in the embryo development problem for the Drosophila melanogaster

In the embryo development problem for the Drosophila melanogaster, a set of molecules known as mor-phogens are responsible for the embryo segmentation. These morphogens are encoded by different genes, including the GAP genes, maternal coordination genes and pair-rule genes. One of the maternal coordination genes encodes the Bicoid morphogen, which is the responsible for the development of the Drosophila embryo at the anterior part and for the control and regulation of the GAP genes in segmentation of the early development of the Drosophila melanogaster. The work presented in this document, reports a methodology that tends to integrate mechanistic and data driven based models, aiming at making inference over the mRNA Bicoid from gene expression data at the protein level for the Bicoid morphogen. The fundamental contribution of this work is the description of the concentration gradient of the Bicoid morphogen in the continuous spatio-temporal domain as well as the output regression (gene expression at protein level) using a Gaussian process described by a mechanistically inspired covariance function. Regression results and metrics computed for the Bicoid protein expression both in the temporal and spatial domains, showed outstanding performance with respect to reported experiments from previous studies. In this paper, a correlation coefficient of r = 0.9758 against a correlation coefficient of r = 0.9086 is being reported, as well as a SMSE of 0.0303±0.1512 against a SMSE of 0.1106±0.5090 and finally reporting a MSLL of −1.7036 ± 1.3472 against −1.0151±1.7669.