Cancer heterogeneity is defined by normal cellular trade-offs.

Gene expression predicts tumor characteristics such as resistance to anticancer therapy. However, generalizing these predictors to multiple cancer types and data sets to motivate new therapeutic strategies has proven difficult. Here, we present a nonnegative matrix factorization (NMF) approach that decomposes gene expression into a universal set of "archetype" fingerprints. By restricting our analysis to five well-defined biological pathways, we show that trade-offs between normal tissues constrain oncogenic heterogeneity. Thus, the resulting six archetypes unify gene expression variation across 54 tissue types, 1504 cancer cell lines, and 1770 patient samples. The archetype mixtures correlate with cancer cell line sensitivity to several common anticancer therapies, even among cancers of the same type. They also explain subtype-specific breast cancer characteristics and define poor prognostic subgroups in breast, colorectal, and pancreatic cancers. Overall, the approach offers an evolvable resource for understanding commonalities across cancers, which could eventually lead to more robust therapeutic strategies.