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Genome conformation underlies transcriptional regulation by distal enhancers, and genomic rearrangements in cancer can alter critical regulatory interactions. Here we profiled the three-dimensional genome architecture and enhancer connectome of 69 tumor samples spanning 15 primary human cancer types from The Cancer Genome Atlas. We discovered the following three archetypes of enhancer usage for over 100 oncogenes across human cancers: static, selective gain or dynamic rewiring. Integrative analyses revealed the enhancer landscape of noncancer cells in the tumor microenvironment for genes related to immune escape. Deep whole-genome sequencing and enhancer connectome mapping provided accurate detection and validation of diverse structural variants across cancer genomes and revealed distinct enhancer rewiring consequences from noncoding point mutations, genomic inversions, translocations and focal amplifications. Extrachromosomal DNA promoted more extensive enhancer rewiring among several types of focal amplification mechanisms. These results suggest a systematic approach to understanding genome topology in cancer etiology and therapy.