Using biologically interrelated experiments to identify pathway genes in Arabidopsis

Motivation: Pathway genes are considered as a group of genes that work cooperatively in the same pathway constituting a fundamental functional grouping in a biological process. Identifying pathway genes has been one of the major tasks in understanding biological processes. However, due to the difficulty in characterizing/inferring different types of biological gene relationships, as well as several computational issues arising from dealing with high-dimensional biological data, deducing genes in pathways remain challenging. Results: In this work, we elucidate higher level gene-gene interactions by evaluating the conditional dependencies between genes, i.e. the relationships between genes after removing the influences of a set of previously known pathway genes. These previously known pathway genes serve as seed genes in our model and will guide the detection of other genes involved in the same pathway. The detailed statistical techniques involve the estimation of a precision matrix whose elements are known to be proportional to partial correlations (i.e. conditional dependencies) between genes under appropriate normality assumptions. Likelihood ratio tests on two forms of precision matrices are further performed to see if a candidate pathway gene is conditionally independent of all the previously known pathway genes. When used effectively, this is a promising approach to recover gene relationships that would have otherwise been missed by standard methods. The advantage of the proposed method is demonstrated using both simulation studies and real datasets. We also demonstrated the importance of taking into account experimental dependencies in the simulation and real data studies.