In order to drive complex biological processes, genes work in a coordinated fashion and often differentially express depending on the environmental factors. The gene DE states are not independent among genes as they have physical and functional relationships. We use Poisson-Gamma-Beta joint density to model the RNA-seq gene expression levels where Beta distribution captures the fold-change between two biological conditions. Moreover, we introduce a three-state Markov Random Field (MRF) model to model the dependency of the DE patterns on the gene network. We integrated known biological pathways and interactions data to our statistical model by forming the neighborhood structure, where we define genes to be first-order neighbors if they are recorded as having direct physical interaction within the interaction database. In general, any database that contains network/interaction information can be used to form the neighborhood structure.
More precisely, our proposed Poisson-Gamma-Beta MRF model assumes the probability of a gene being DE will increase if the gene is surrounded by a higher proportion of neighboring genes that are also DE. On the other hand, if the gene is surrounded by a higher proportion of equally expressed (EE) neighboring genes, then the probability of that gene being DE will also decrease.