Abstract
We propose a novel conditional graphical model - spaceMap - to construct gene regulatory networks from multiple types of high dimensional omic profiles. A motivating application is to characterize the perturbation of DNA copy number alterations (CNAs) on downstream protein levels in tumors. Through a penalized multivariate regression framework, spaceMap jointly models high dimensional protein levels as responses and high dimensional CNAs as predictors. In this setup, spaceMap infers an undirected network among proteins together with a directed network encoding how CNAs perturb the protein network. spaceMap can be applied to learn other types of regulatory relationships from high dimensional molecular profiles, especially those exhibiting hub structures. Simulation studies show spaceMap has greater power in detecting regulatory relationships over competing methods. Additionally, spaceMap includes a network analysis toolkit for biological interpretation of inferred networks. We applies spaceMap to the CNAs, gene expression and proteomics data sets from CPTAC-TCGA breast (n=77) and ovarian (n=174) cancer studies. Each cancer exhibits disruption of 'ion transmembrane transport' and 'regulation from RNA polymerase II promoter' by CNA events unique to each cancer. Moreover, using protein levels as a response yields a more functionally-enriched network than using RNA expressions in both cancer types. The network results also help to pinpoint crucial cancer genes and provide insights on the functional consequences of important CNA in breast and ovarian cancers. The R package spaceMap - including vignettes and documentation - is hosted on https://topherconley.github.io/spacemap.