Molecular phenotyping using networks, diffusion, and topology: soft tissue sarcoma
Many biological datasets are high-dimensional yet manifest an underlying order. In this paper, we describe an unsupervised data analysis methodology that operates in the setting of a multivariate dataset and a network which expresses influence between the variables of the given set. The technique involves network geometry employing the Wasserstein distance, global spectral analysis in the form of diffusion maps, and topological data analysis using the Mapper algorithm. The prototypical application is to gene expression profiles obtained from RNA-Seq experiments on a collection of tissue samples, considering only genes whose protein products participate in a known pathway or network of interest. Employing the technique, we discern several coherent states or signatures displayed by the gene expression profiles of the sarcomas in the Cancer Genome Atlas along the p53 signaling network. The signatures substantially recover the leiomyosarcoma, dedifferentiated liposarcoma (DDLPS), and synovial sarcoma histological subtype diagnoses, but they also include a new signature defined by simultaneous activation and inactivation of about a dozen genes, including activation of fibrinolysis inhibitor SERPINE1/PAI and inactivation of p53-family tumor suppressor gene P73 along with cyclin dependent kinase inhibitor 2A CDKN2A/P14ARF.