A skellam model to identify differential patterns of gene expression induced by environmental signals

RNA-seq, based on deep-sequencing techniques, has been widely employed to precisely measure levels of transcripts and their isoforms expressed under different conditions. However, robust statistical tools used to analyze these complex datasets are lacking. By grouping genes with similar expression profiles across treatments, cluster analysis provides insight into gene functions and networks that have become increasingly important.

We proposed and verified a cluster algorithm based on a skellam model for grouping genes into distinct groups based on the pattern of gene expression in response to changing conditions or in different tissues. This algorithm capitalizes on the skellam distribution to capture the count property of RNA-seq data and clusters genes in different environments. A two-stage hierarchical expectation-maximization (EM) algorithm was implemented to estimate the optimal number of groups and mean expression levels of each group across two environments. A procedure was formulated to test whether and how a given group shows a plastic response to environmental changes. The model was used to analyze an RNA-seq dataset measured from reciprocal crosses of early Arabidopsis thaliana embryos that respond differently based on the extent of maternal and paternal genome contributions, from which genes associated with maternal and paternal contributions were identified. Simulation studies were also performed to validate the statistical behavior of the model.

This model is a useful tool for clustering gene expression data by RNA-seq, thus facilitating our understanding of gene functions and networks.