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A key mutational process in cancer is structural variation, in which rearrangements delete, amplify or reorder genomic segments ranging in size from kilobases to whole chromosomes. We developed methods to group, classify and describe structural variants, applied to >2,500 cancer genomes. Nine signatures of structural variation emerged. Deletions have trimodal size distribution; assort unevenly across tumour types and patients; enrich in late-replicating regions; and correlate with inversions. Tandem duplications also have trimodal size distribution, but enrich in early-replicating regions, as do unbalanced translocations. Replication-based mechanisms of rearrangement generate varied chromosomal structures with low-level copy number gains and frequent inverted rearrangements. One prominent structure consists of 1-7 templates copied from distinct regions of the genome strung together within one locus. Such cycles of templated insertions correlate with tandem duplications, frequently activating the telomerase gene, TERT, in liver cancer. Cancers access many rearrangement processes, flexibly sculpting the genome to maximise oncogenic potential.

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