Approximation algorithms
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Breast cancer is the most common malignancy and a leading cause of cancer related deaths in women. In recent years, gene expression profiling has proved useful in delineating molecular subtypes of breast cancer and in the development of prognostic signatures. We are developing an analytical pipeline to characterize the transcriptional regulators of these subtypes and signatures. Our approach complements current bioinformatics approaches for transcription factor analysis with a vertex cover algorithm on hypergraphs. We utilize this approach to build a network of differentially expressed genes in a tumor subtype or based on a predefined signature and the candidate transcription factors regulating these genes. Maximum cardinality and minimum weight vertex covers in hypergraphs are used to choose a set of candidate transcription factors that (1) are provably within a small factor of the optimum cover, and (2) are the key regulators of disease pathogenesis. Our model can then be used to predict the most important transcription factors regulating the network. We then use this approach to find modules or combinations of transcription factors regulating different functional subsets of genes. We test our approach using data generated with cell lines in the context of estrogen receptor mediated transcription and demonstrate that we can recover previously known or expected regulators. Then, we apply the method to a primary breast cancer cohort partitioned into two groups with prognostic differences defined by high or low levels of an insulin-like growth factor gene expression signature. These results suggest the method has the potential to identify transcription factors regulating different molecular subtypes of breast cancer.