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

TL;DR

This paper develops and compares two physically-inspired Gaussian process models based on reaction-diffusion equations to analyze post-transcriptional regulation in Drosophila, avoiding spatial discretization and leveraging kernel differentiation.

Contribution

It introduces a novel GP model that simplifies reaction-diffusion modeling by only differentiating kernels, enhancing analysis of gene regulation without spatial discretization.

Findings

Both models accurately predict gene expression patterns.

The novel model performs comparably to previous methods.

Models are effective with limited mRNA data.

Abstract

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