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We introduce hybrid BAG-seq: a high-throughput, multi-omic method that simultaneously captures DNA and RNA from single nuclei. We apply this protocol to 65,499 single nuclei from samples of five uterine cancer patients and validate the clustering using RNA-only and DNA-only protocols from the same tissues. Multiple tumor genome or expression clusters are often present within a patient, with different tumor clones projecting into distinct or shared expression states, demonstrating nearly all possible genome-transcriptome correlations. We also identify mutant stroma with significant X chromosome loss in various cell types and patient-specific stromal subtypes exhibiting aberrant expression patterns.