Physically-Inspired Gaussian Process Models for Post-Transcriptional\n Regulation in Drosophila

Abstract

The regulatory process of Drosophila is thoroughly studied for understanding\na great variety of biological principles. While pattern-forming gene networks\nare analysed in the transcription step, post-transcriptional events (e.g.\ntranslation, protein processing) play an important role in establishing protein\nexpression patterns and levels. Since the post-transcriptional regulation of\nDrosophila depends on spatiotemporal interactions between mRNAs and gap\nproteins, proper physically-inspired stochastic models are required to study\nthe link between both quantities. Previous research attempts have shown that\nusing Gaussian processes (GPs) and differential equations lead to promising\npredictions when analysing regulatory networks. Here we aim at further\ninvestigating two types of physically-inspired GP models based on a\nreaction-diffusion equation where the main difference lies in where the prior\nis placed. While one of them has been studied previously using protein data\nonly, the other is novel and yields a simple approach requiring only the\ndifferentiation of kernel functions. In contrast to other stochastic\nframeworks, discretising the spatial space is not required here. Both GP models\nare tested under different conditions depending on the availability of gap gene\nmRNA expression data. Finally, their performances are assessed on a\nhigh-resolution dataset describing the blastoderm stage of the early embryo of\nDrosophila melanogaster\n