In this article we propose a Bayesian hierarchical model for the identification of differentially expressed genes in Daphnia magna organisms exposed to chemical compounds, specifically munition pollutants in water. The model we propose constitutes one of the very first attempts at a rigorous modeling of the biological effects of water purification. We have data acquired from a purification system that comprises four consecutive purification stages, which we refer to as "ponds," of progressively more contaminated water. We model the expected expression of a gene in a pond as the sum of the mean of the same gene in the previous pond plus a gene-pond specific difference. We incorporate a variable selection mechanism for the identification of the differential expressions, with a prior distribution on the probability of a change that accounts for the available information on the concentration of chemical compounds present in the water. We carry out posterior inference via MCMC stochastic search techniques. In the application, we reduce the complexity of the data by grouping genes according to their functional characteristics, based on the KEGG pathway database. This also increases the biological interpretability of the results. Our model successfully identifies a number of pathways that show differential expression between consecutive purification stages. We also find that changes in the transcriptional response are more strongly associated to the presence of certain compounds, with the remaining contributing to a lesser extent. We discuss the sensitivity of these results to the model parameters that measure the influence of the prior information on the posterior inference.
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- Bayesian inference, Daphnia magna, Environmental toxicology, Probit prior, Transcriptomics, Variable selection