The regulatory process of Drosophila has been thoroughly studied for understanding a great variety of systems biology principles. While pattern-forming gene networks are further 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 post-transcriptional regulation of gap genes in Drosophila depends on spatiotemporal interactions between mRNAs and gap proteins, proper physically-inspired stochastic models are required to study the existing link between both quantities. Previous research attempts have shown that the use of Gaussian processes (GPs) and differential equations leads 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 on whether the GP prior is placed. While one of them has been studied previously using gap protein data only, the other is novel and yields a simplistic 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.