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Copy number aberrations are recognized to be important in cancer as they may localize to regions harboring oncogenes or tumor suppressors. Such genomic alterations mediate phenotypic changes through their impact on expression. Both cis- and transacting alterations are important since they may help to elucidate putative cancer genes. However, amidst numerous passenger genes, trans-effects are less well studied due to the computational difficulty in detecting weak and sparse signals in the data, and yet may influence multiple genes on a global scale. We propose an integrative approach to learn a sparse interaction network of DNA copy-number regions with their downstream transcriptional targets in breast cancer. With respect to goodness of fit on both simulated and real data, the performance of sparse network inference is no worse than other state-of-the-art models but with the advantage of simultaneous feature selection and efficiency. The DNA-RNA interaction network helps to distinguish copy-number driven expression alterations from those that are copy-number independent. Further, our approach yields a quantitative copy-number dependency score, which distinguishes cis-versus trans-effects. When applied to a breast cancer data set, numerous expression profiles were impacted by cis-acting copy-number alterations, including several known oncogenes such as GRB7, ERBB2, and LSM1. Several trans-acting alterations were also identified, impacting genes such as ADAM2 and BAGE, which warrant further investigation. Availability: An R package named lol is available from www.markowetzlab.org/software/lol.html.