Tensors and algebra give interpretable groups for crosstalk mechanisms in breast cancer

We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from multidimensional arrays of experimental data. Our methodology is applicable to high dimensional data structures that arise across the sciences. Specifically we introduce a new way to cluster data subject to multi-indexed structural constraints via integer programming. The method can work as a stand-alone clustering tool or in combination with established methods. We implement this approach on a dataset consisting of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand. The data consist of time-course measurements of the immediate-early signaling of mitogen activated protein kinase (MAPK), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT). By respecting the multi-indexed structure of the experimental data, the analysis can be optimized for biological interpretation and therapeutic understanding. We quantify the heterogeneity of breast cancer cell subtypes and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method.