Author Correction: Patterns of somatic structural variation in human cancer genomes

A key mutational process in cancer is structural variation, in which rearrangements delete, amplify or reorder genomic segments that range in size from kilobases to whole chromosomes1–7. Here we develop methods to group, classify and describe somatic structural variants, using data from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA), which aggregated whole-genome sequencing data from 2,658 cancers across 38 tumour types8. Sixteen signatures of structural variation emerged. Deletions have a multimodal size distribution, assort unevenly across tumour types and patients, are enriched in late-replicating regions and correlate with inversions. Tandem duplications also have a multimodal size distribution, but are enriched in early-replicating regions—as are 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 2–7 templates copied from distinct regions of the genome strung together within one locus. Such cycles of templated insertions correlate with tandem duplications, and—in liver cancer—frequently activate the telomerase gene TERT. A wide variety of rearrangement processes are active in cancer, which generate complex configurations of the genome upon which selection can act. Whole-genome sequencing data from more than 2,500 cancers of 38 tumour types reveal 16 signatures that can be used to classify somatic structural variants, highlighting the diversity of genomic rearrangements in cancer.

Mutations that arise in somatic cells are the driving force of cancer development. Structural variation-in which genomic rearrangement acts to amplify, delete or reorder chromosomal material at scales that range from single genes to entire chromosomes-is an especially important class of somatic mutation. Previous analyses of both cancer and germline genomes have enabled the description of several distinctive patterns of structural variants [1][2][3][4][5][6][7] , and hypotheses about the underlying basis of several of these patterns have been proposed on the basis of their clustering, orientation and associated copy-number changes. Hypothesis-driven in vitro studies are now beginning to reveal some of the mechanistic processes that generate these structures [9][10][11][12][13] , and generate further predictions that can be assessed in the genomic data. However, the landscape of structural variation in human cancer remains incompletely mapped and there are many complex structures that elude formal description.
The PCAWG Consortium aggregated whole-genome sequencing data from 2,658 cancers across 38 tumour types, generated by the ICGC and TCGA projects. These sequencing data were aligned to the human genome (reference build hs37d5) and analysed with standardized, highaccuracy pipelines to call somatic and germline variants of all classes 8 . Here, we analyse the patterns and signatures of structural variants across the PCAWG data. We propose a working classification scheme that encompasses known and newly identified classes of structural variants. We develop methods for annotating the observed structural variants in a given cancer genome, identifying a class of replication-based rearrangement processes that generate clusters of several structural variants. We explore the size, activity and genome-wide distribution of classifiable structural variant types across the cohort, using signature analysis to define how they correlate within patients. Other papers produced by PCAWG address complementary aspects of structural variants, including inference of positive selection acting on recurrently rearranged regions of the genome 14 , how structural variants affect the transcriptome 15 and chromosome topology 16 , patterns of somatic retrotransposition 17 and distribution of chromothripsis across cancer types 18 .

Classification of structural variants
A 'structural variant' manifests as a 'junction' between two 'breakpoints' in the genome (terms in inverted commas here and below refer to those defined in the glossary in Extended Data Table 1). Generally, there will be a change in copy number across a given breakpoint if only one side of the break is rescued by a structural variant; if both sides of a doublestranded DNA break are rescued, a 'reciprocal' or 'balanced' structural variant will result, without substantial copy-number change. We sometimes observe 'clusters of structural variants' in which several breakpoints occur close together, in time or in genomic space-usually both. Such spatial and/or temporal proximity generally, but not always, implies that the structural variants within a cluster are mechanistically linked. Clusters can be 'phased' (in which case all structural variants in the cluster resolve to a single derivative chromosome) or 'unphased', in which case the structural variants are carried on different derivative chromosomes. An example of the latter is a reciprocal translocation that results in two derivative chromosomes, each with a single interchromosomal breakpoint junction (Fig. 1).
We recognize distinct 'classes of structural variant' from the orientation of the two segments at the junction and associated copy-number changes ( Fig. 1, Supplementary Fig. 1). Some classes of structural variant (such as isochromosomes and rearrangements between extended, highly homologous sequences) are difficult to detect with short-read sequencing data; these classes are not considered further here. We propose categorizing classes of structural variant across two facets: the number of breakpoints involved (simple or complex) and by whether the patterns are likely to arise from 'cut-and-paste' or 'copy-and-paste' rearrangement processes. A cut-and-paste process generates a cluster of structural variants consistent with reshuffling or loss of extant genomic segments, and a copy-and-paste process is one in which copies of genomic 'templates' are newly replicated or synthesized and inserted during the rearrangement process. Deletions, reciprocal inversions, unbalanced translocations and reciprocal translocations are examples of simple cut-and-paste structural variants, as they can be reconstructed from the incorrect religation of chromosomal breaks. Tandem duplications are simple copy-and-paste structural variants, as they arise through the local insertion of a newly generated extra copy of a genomic template.
More-complex cut-and-paste processes that produce structural variants also occur in cancer. 'Breakage-fusion-bridge' events result from cycles of DNA breakage, end-to-end sister chromatid fusions, mitotic bridges and further DNA breakage. These events manifest as one or a few proximate, inverted breakpoint junctions with associated copy-number change, which we call 'fold-back inversions' 1,2,19 (Fig. 1). 'Chromoplexy' 5,20 -which is particularly frequent in prostate cancersresults from several simultaneous double-stranded DNA breaks in several chromosomes that are rejoined incorrectly, leading to balanced chains of rearrangements. 'Chromothripsis' 3 , in which chromosome shattering and rearrangement occur in a single catastrophic event 9,21 , leads to a pattern of oscillating copy-number changes and localized clustering of tens to hundreds of breakpoints 22 .
In the germline, more-complex copy-and-paste classes of structural variant have previously been described, which involve small duplications and triplications and are thought to arise from the stalling of the replication fork leading to template switching 4,23,24 . Here we describe a wide range of complex copy-and-paste types of somatic structural variant that occur in human cancers, and that are typically characterized by copy-number gains and frequent inverted rearrangements.

Annotation of structural-variant classes
We analysed 2,559 whole cancer genomes across 38 tumour types (alongside matched germline DNA) that passed the most stringent PCAWG quality-control criteria: 1 or more somatic structural variants were detected in 2,429 tumours 8 . As described in an accompanying Article 8 , structural variants were identified using aberrantly mapping and/or split reads in paired-end sequencing data 25 . We used four somatic structural-variant callers 20,[25][26][27] , and the final structural-variant dataset comprised events that were returned by ≥2 callers, merged by a graph-based consensus method 8 . We consider only somatically acquired structural variants in this analysis, and exclude somatic retrotransposition events. Validation of structural-variant calls was undertaken using both manual inspection and pull-down with resequencing of breakpoints. With these approaches, we estimate the sensitivity of the consensus structural-variant call set to be 90% for true calls generated by any 1 of the 4 callers; specificity was estimated as 97.5% 8 . A mean of 3.22 algorithms of the 4 that we used called each structural variant in the consensus set genome-wide, and this differed little across repetitive elements: the mean for short interspersed nuclear elements was 3.22, and the mean for long interspersed nuclear elements was 3.21.
Because the structural variants from a given cancer are often highly clustered, we grouped rearrangements into clusters on the basis of the  Fig. 1 | Classification of structural variants in cancer genomes. Schematics of major structural-variant (SV) classes, grouped according to whether they are simple or complex and arise through cut-and-paste or copy-and-paste processes. Each schematic comprises three parts. The top segment shows dotted arcs for each rearrangement junction that joins two chromosomal segments together. The middle segment shows the copy number of genomic segments that are involved. The bottom segment shows the configuration of the final derivative chromosome that results from the structural variant; the colour of the segments corresponds to the colour of that segment in the copynumber schematic. + indicates the different derivative chromosomes created for some of the classes: that is, the structural variants are not phased to a single derivative.
Article proximity of breakpoints, the overall number of events in that genome and the size distribution of these events (Supplementary Methods). Essentially, a particular cluster contains structural variants that are significantly closer together than expected by chance, given the overall number and orientation of structural variants in that patient. Alongside the clustering, we computed an in silico library of all possible genomic configurations that result from sequential simple structural variants (deletions, tandem duplications, inversions, translocations, and chromosome duplications or losses), to a depth of five rearrangements. We could then compare the genomic configuration of each observed cluster of structural variants against the library to determine how it might have arisen. This methodology has the advantage that breakpoint junctions are classified according to the wider genomic context in which they occur. This means that, for example, true deletions will be identifiably different from breakpoint junctions that happen to have a deletion-type orientation but arise within (for instance) a chromothripsis event of markedly different mechanism and properties. Over half the breakpoint junctions that we observed arise within clusters of several or many structural variants (Fig. 2a): removing these junctions from the catalogues of true deletions, tandem duplications and inversions enables a more-precise description of the properties of simple structural variants.
Among the classes of simple structural variants, deletion was the most common, followed by tandem duplication and then unbalanced translocation. Reciprocal translocations and reciprocal inversions were uncommon events (Fig. 2a). There was considerable variability in the overall numbers and distribution of classes of structural variant across tumour types and across patients within a given tumour type (Extended Data Fig. 1). For example, oesophageal adenocarcinomas were characterized by many deletions and a large number of complex clustered rearrangements (Fig. 2b), and ovarian cancers often carried high numbers of tandem duplications and/or deletions with moderate numbers of unbalanced translocations (Fig. 2c).

Cycles of templated insertions
We next examined clusters that contain 2-10 structural variants. One newly identified configuration consisted of several segments of copynumber gains, typically on different reference chromosomes, linked together through structural variants (Fig. 3,Extended Data Fig. 2). A sequential path through consecutive segments can be formed by following the breakpoint junctions, which suggests that each cluster represents a string of duplicated templates inserted into a single derivative chromosome, probably acquired concurrently. Although it is theoretically possible that the structural variants in such clusters are not phased on the same derivative chromosome or do not occur concurrently, we think this is unlikely for several reasons. First, we found examples of RNA transcripts that spliced together exons separated by two junctions in the structural-variant cluster ( Supplementary  Fig. 2), which suggests that they are phased on the same derivative chromosome. Second, long-read sequencing data (reported in an accompanying Article 8 ) supported the phasing of structural variants that link templated insertions. Third, we found that the clonal fraction of tumour cells tended to be more similar for structural variants within these clusters than for randomly chosen structural variants in each patient ( Supplementary Fig. 3), which suggests that they cooccur in evolutionary time. Fourth, the level of copy-number gain for individual segments in the cluster tended to be identical (Fig. 3,Extended Data Fig. 2).
We define three basic categories on the basis of whether or not the string of inserted segments returns to the original chromosome: we term strings of inserted segments that do not return 'chains' of templated insertions and those strings that do return 'bridges' (which leave a gap on the host chromosome) or 'cycles' (which rereplicate a segment on the host chromosome). In the PCAWG dataset overall, we observed 1,467 cycles and 1,275 bridges of templated insertions (Fig. 3a,b,Extended Data Fig. 2). In chains of templated insertions, the string of genomic segments does not return to the chromosome of departure (Fig. 3c, Extended Data Fig. 2) but it is similarly associated with copy-number gains at each templated segment. There were 285 instances of such chains in the dataset, commonly manifesting as unbalanced translocations joined through one or more intermediary templated insertions.
Most templated insertion events involve only two breakpoint junctions, but this can extend to three, four or more linked rearrangements (Extended Data Fig. 3a). The longest such event-from a cervical squamous cell cancer-had seven templated insertions strung together on an eighth host chromosome ( Fig. 3c; other examples of long templated insertion events are shown in Extended Data Fig. 3).  Within each tumour type, the frequency distribution (y axis) of different structural-variant categories (x axis) across patients is shown as a density: regions of highest density have the greatest width of shaded area. In each panel, the number of patients is indicated at the top right. AdenoCA, adenocarcinoma; BNHL, B-cell non-Hodgkin lymphoma; ChRCC, chromophobe renal cell carcinoma; CLL, chronic lymphocytic leukaemia; CNS, central nervous system; GBM, glioblastoma; HCC, hepatocellular carcinoma; leiomyo, leiomyosarcoma; medullo, medulloblastoma; MPN, myeloproliferative neoplasm; eso, oesophageal; oligo, oligodendrocytic; panc, pancreatic; piloastro, pilocytic astrocytoma; prost, prostate; RCC, renal cell carcinoma; sarc, sarcoma; SCC, squamous cell carcinoma; TCC, transitional cell carcinoma; thy, thyroid. b, Per-sample counts of complex (bottom) and classified (top) structural-variant breakpoint junctions for oesophageal adenocarcinoma. c, Per-sample counts of complex (bottom) and classified (top) structural-variant breakpoint junctions for ovarian adenocarcinoma.

Templated insertions that affect TERT
Structural variants drive tumour development through their effects on cancer genes, whether by altering gene copy number, disrupting tumour-suppressor genes, creating fusion genes or juxtaposing the coding sequence of one gene with the regulatory apparatus of another. We found that many liver cancers had cycles of templated insertions that affect TERT (Fig. 3d, e, Extended Data Fig. 4). Point mutations in the TERT promoter are present in 54% of liver cancers, and a further 5-10% of liver cancers have structural variants that activate the gene 28 . Of the 30 patients with liver cancer that had structural variants that affect TERT, we find that 10 of these variants were templated insertion events (mostly cycles). All of these events duplicated the entire TERT gene and linked it to duplications of whole genes, fragments of genes or regulatory elements from elsewhere in the genome, and led to increased expression of TERT (Extended Data Fig. 4e). Thus, this particular rearrangement process is distinctive for the precision with which cancer copy-and-pastes normally disparate functional elements of its genome together without wholesale instability.
Tumour-suppressor genes were also inactivated by templated insertions (Extended Data Fig. 5). For example, among many straightforward deletions, RB1 was hit by cycles of templated insertions, a templated insertion with deletion and one instance of the linked, inverted duplications detailed in 'Local n-jumps and local-distant clusters'. These events typically generated duplications of internal exons in RB1 and/or  Fig. 1, with structural variants shown as dotted arcs linking two copy-number segments. The derivative chromosome(s) that could explain the copy-number and structural-variant profile is shown below. d, e, Cycles of templated insertions that affect the TERT gene, in two hepatocellular carcinomas. KIAA1024 is also known as MINAR1.
Article insertions of exons from other genes, all of which presumably rendered a non-functional transcript.

Local n-jumps and local-distant clusters
Many clusters of 2-10 structural variants in the dataset were confined to a single genomic region. Of those clusters that comprised two local rearrangements, some had straightforward explanations, such as nested or adjacent tandem duplications. However, many did not have a trivial explanation (Fig. 4a). These included a duplication-invertedtriplication-duplication structure that has previously been observed in germline structural variants 24 (349 instances); a structure of two duplications linked by inverted rearrangements (531 instances); and structures of copy-number loss plus nearby duplication linked by inverted rearrangements (472 instances). All of these patterns had solutions in which breakpoints were phased to a single derivative chromosome (Fig. 4a), although non-phased solutions are theoretically possible (if unlikely). Beyond clusters of two rearrangements (two-jumps), we also found examples involving three, four or more rearrangements confined to one genomic locale (Fig. 4b). All of these configurations of clusters of structural variants can be phased to a single derivative chromosome, with tightly grouped breakpoints.
Beyond clusters confined to a single genomic region, we found clusters of 2-10 structural variants that combined local jumps with rearrangements that reach into one or more distant regions of the genome (Fig. 4c). Simple examples of these events include unbalanced translocations or large deletions with a locally derived fragment inserted at the breakpoint, but there was also an extensive range of more-complex patterns. In some cases, the source of the inserted fragment was distal to the major break, and the structural variant could feasibly result from several concurrent DNA breaks in close spatial proximity to the capture of a short DNA fragment during repair (cut-and-paste). In other cases, the origin of the inserted fragment was proximal to the major break and associated with a gain in copy number. This pattern is difficult to explain by a cut-and-paste mechanism, because the copy-number gain implies the inserted segment was a duplicate of the original template rather than a separated fragment redistributed from its original locus. Instead, a copy-and-paste

Fig. 5 | Size distribution and genomic properties of classified structural
variants. a, Size distribution of deletions per histology group, with tumour types ordered according to total number of events seen. Vertical dashed lines represent the two prominent modes. b, Size distribution of segments of templated insertion per histology group. For each tumour type, the three distributions for cycles, bridges and chains of templated insertions are superimposed. Ins, insertion. c, Associations between a subset of the genomic properties (rows) and classes of structural variant (columns). Each density curve represents the quantile distribution of the genomic property values at observed breakpoints compared to random genome positions. Asterisks indicate a significant departure from uniform quantiles after multiple hypothesis correction on a one-sided Kolmogorov-Smirnov test based on a sample size of 2,559 genomes containing structural variants: *false-discovery rate < 0.01, **false-discovery rate < 0.001, ***false-discovery rate < 10 −6 . Cells with significant property associations are shaded by the magnitude of the shift of the median observed quantile above (blue) or below (red) 0.5. The interpretation of each property from left to right is indicated by the axes to the right of the property label. Complex uncl, complex clusters unclassified; cplxy, chromoplexy; del, deletion; inv, inversion; ins, insertion; LAD, laminaassociated domain; recip, reciprocal; TAD, topologically associated domain; TD, tandem duplication; trans, translocation; unbal, unbalanced. d, Rearrangement counts as a function of bases of junction microhomology, fit to three linear functions consistent with different formation mechanisms. NHEJ, non-homologous end joining; MMEJ, microhomology-mediated end joining; SSA, single-strand annealing. e, Enrichment or depletion of breakpoint junctions between regions of the genome with particular annotations, compared with a permuted background that preserves breakpoint positions but swaps breakpoint partners. Centre points are the mean fold change over the permuted background; error bars represent three s.d. Analysis is based on a sample size of 2,559 genomes containing structural variants. LTR, long terminal repeat; SINE, short interspersed nuclear element; LINE, long interspersed nuclear element; heterochrom, heterochromatin.
Article mechanism may be the more parsimonious explanation for these events.
A comparison of local footprints linked together through distant rearrangements revealed a strong connectivity of footprints with the same or similar structure, often enriched tenfold or more than expected by chance (see 'Footprint connectivity analysis' in Supplementary Results). The reasons for this are unclear, but it may reflect innate structural symmetry introduced through the generation or the resolution of rearrangements, or through the repeated action of a mechanism that imparts consistent structural motifs.

Copy-and-paste patterns of clusters
The diverse patterns of 2-10 clustered structural variants (Figs. 3,4) share important morphological features: (1) genomic configurations that can be phased to a single derivative chromosome; (2) low-level gains in copy number, especially duplications and triplications; (3) a high frequency of inverted rearrangements in addition to noninverted rearrangements; (4) occurrence on a chromosome background with similar average copy number to the tumour overall; and (5) tight proximity of breakpoints within the local footprint (typically <1 Mb).
Using our in silico library of genomic configurations, we could define all possible routes by which sequential structural variants could generate these structures through the classically defined repertoire of deletion, tandem duplication, inversion and translocation ( Supplementary  Fig. 4). These routes typically would require implausible machinations of chromosomes (Supplementary Results). In particular, the high prevalence of inverted breakpoint junctions and local copy-number gains is difficult to recreate using sequential simple rearrangements. Simple inversion events are uncommon in cancers (Fig. 1d) and they tend not to generate copy-number gains, except through breakage-fusion-bridge cycles: these latter also cause terminal deletions 2 , which are not seen in the events discussed here.
If these events cannot be satisfactorily explained by sequential simple rearrangements, another possible explanation is a complex cut-and-paste mechanism such as chromothripsis, chromoplexy or repeated breakage-fusion-bridge cycles. However, the patterns of the 2-10 clustered structural variants do not fit with these processes either (Supplementary Results). Although chromothripsis with copynumber gain has previously been described 3,11,19,22 , the resulting copy number and rearrangement patterns have different properties to those we observed. Chromoplexy, in which chromosome breaks lead to a balanced interchange at multiple breakpoint junctions 5,20 , typically generates unphased solutions. Repeated breakage-fusion-bridge cycles tend to cause high-level copy-number gains associated with inverted, fold-back rearrangements 1,2 , unlike the structures reported here.
Instead, we believe that many of these locally complex clusters of structural variants with low-level copy-number gains are generated in a single event by a copy-and-paste process. That is, the copying of genomic templates is an intrinsic aspect of the structural variation process in these events, with the extra copies being inserted in the resulting derivative chromosome. If the genomic templates all originate locally, we would observe local n-jumps (such as in Fig. 3a, b) with a tight clustering of breakpoints, phased solutions, frequent copy-number gains and a mix of inverted and noninverted breakpoint junctions. If the original templates for the copied segments derive from across the genome, chains, cycles and bridges of templated insertions would arise (Fig. 2).

Genomic properties of structural variants
The size of tandem duplications and deletions followed complex-often multimodal-distributions across tumour types (Fig. 5a, Extended Data Fig. 6a). However, as previously reported 6,29 , individual patients tend to have a simpler-usually unimodal-distribution of deletions or tandem duplications (Extended Data Fig. 6b), which implies that the complexity seen in a given tumour type results from combining samples with different profiles. The sizes of individual fragments in templated insertion events were also distinctly multimodal, with varying peak heights across tumour types (Fig. 5b). When correlating template sizes within a given event, two patterns emerged: one in which template sizes were closely correlated with one another, and one in which a small (<1 kb) template was linked with one of any size (Extended Data Fig. 7a,  b). Likewise, the sizes of segments within a given local two-jump event showed moderately strong correlations with one another (Extended Data Fig. 7c).
A number of genomic properties (such as replication timing, transcriptional activity and chromatin state) influence the density of point mutations 30,31 and copy-number alterations 32 , but how this relates to individual classes of structural variant is unclear. From the literature, we compiled a library of the genome-wide distribution of 38 features including replication timing, GC content, repeat density, gene density and distance to G-quadruplex motifs, among others. Replication timing had the strongest association with the occurrence of structural variants; deletions are enriched in late-replicating regions, and tandem duplications and unbalanced translocations occur preferentially in early-replicating regions (Fig. 5c,Extended Data Fig. 8). For individual patients with high numbers of deletions or tandem duplications, we observed notable heterogeneity in the distribution of these structural variants according to replication timing: some had events that occurred predominantly in late-replicating regions, others had events that occurred exclusively in early-replicating regions, and in others events were distributed more evenly ( Supplementary Fig. 5). Regions of active chromatin and increased gene density correlated positively with the rate of rearrangement.
A structural variant requires DNA repair pathways to join two sequences together, and several repair mechanisms are available to somatic cells. Some require sequence homology between the two ends, and others can operate to join non-homologous sequences. As previously reported 2,25,33 , we find across the PCAWG data that many structural variants do not have sequence homology at the breakpoint junction ( Fig. 5d) and therefore arise through non-homologous end joining. Nonetheless, a sizable fraction of structural variants has more microhomology than expected by chance, with an apparently bimodal distribution of microhomology lengths. One set of structural variants has 2-7 bp of microhomology, probably generated by microhomology-mediated end joining, and a second set of structural variants has 10-30 bp of microhomology, probably generated through single-strand annealing or other forms of homologous recombination (including microhomology-mediated break-induced replication). Repetitive sequences in the genome, such as short and long interspersed nuclear elements, are the likely substrate of such structural variants, and we find enrichment for structural variants joining such elements (Fig. 5e,  Supplementary Fig. 6).

Signatures of structural variation
The heterogeneous spectrum of point mutations across cancers can be reconstructed from the differential action of a relatively limited repertoire of mutational processes, each with a characteristic signature 34 . The differences across patients in the size distribution of tandem duplication and deletion-together with the widely varying frequency and patterns of structural variant across tumour types and genome topology-suggested that we could similarly learn such correlations across individual classes of structural variant.
We divided the set of structural variants of each patient into mutually exclusive categories. We split the most frequent classes of simple structural variant (deletions and tandem duplications) into 11 categories according to size, replication timing and occurrence at fragile sites. Other configurations of structural variants and copy-number changes seen more than 50 times in the cohort were included as further categories, including cycles, chains and bridges of templated insertions (also split by size), local n-jumps and local-distant clusters.
We applied two methods for signature discovery, which yielded comparable results. We identified 16 structural-variant signatures: the 12 most prevalent of these signatures are shown in Fig. 6a. Signature extraction on the cohort randomly split into two halves identified ten highly correlated signatures ( Supplementary Fig. 7), which closely matched the signatures called in the full cohort despite the lower power. Three signatures of deletions emerged, split by size: the signature of small (<50-kb) deletions included small reciprocal inversions and the signature of large (>500-kb) deletions included large reciprocal inversions. This implies that the frequencies of deletions and reciprocal inversions are correlated across the cohort, and both follow similar size distributions within an individual patient.
We identified five signatures of tandem duplications, split by size and replication timing. Cycles, bridges and chains of templated insertions were particularly prominent in signatures of early-replicating tandem duplications, whereas local two-jump structures were more closely associated with late-replicating tandem duplications. All of these patterns exemplify the copy-and-paste concept, in which extra copies of genomic templates are produced and inserted as an integral feature of the structural-variant process.
Another signature was characterized by deletions and tandem duplications at chromosomal fragile sites 35 . Tandem duplications were more   RAD51B (9) POLE (9) PALB2 (7) MSH (9) FANC (41) CHEK2 (14) CDK12 ( Article prominent at the edges of the fragile site, and deletions were concentrated in the centre (Extended Data Fig. 9a, b). The size range of fragile site deletions peaked at around 100 kb, similar to the larger deletion signature, whereas the rarer fragile-site tandem duplications showed no strong size peak (Extended Data Fig. 9c). Sites of fragility varied extensively across tumour types (Extended Data Fig. 9d). Unbalanced translocations comprised their own signature, which suggests that they derive from a distinct rearrangement process in cancer genomes. A further signature comprised both the fold-back inversions that are a hallmark of breakage-fusion-bridge cycles and similar structures such as translocations adjacent to fold-back inversions. Finally, there was a signature of balanced rearrangements, including reciprocal translocations and chromoplexy clusters 5 . This signature probably arises from several double-stranded DNA breaks (potentially occurring in interphase), in which both sides of the break are incorrectly repaired through ligation to other, simultaneously broken regions of the genome.

DNA repair genes and tumour type
We grouped annotations of pathogenic germline variants and somatic driver mutations in DNA-repair genes across the cohort 8 , correlating their presence with activity of the structural-variant signatures (Fig. 6b). As previously described for breast and ovarian cancers 6,29 , BRCA1 mutations are significantly associated with small tandem duplication signatures, the mechanistic basis of which is increasingly well understood 10 . As previously described 6,36 , CDK12 variants predicted signatures of mid-sized-to-large tandem duplications. BRCA2 variants correlated with small deletions, as expected from previous work 29 , and also with the reciprocal structural-variant signature that includes chromoplexy. PALB2 variants showed the same correlations with signatures of small deletions and reciprocal structural variants as does BRCA2: PALB2 colocalizes with, stabilizes and assists BRCA2 during homologous recombination 37 , so we might have predicted that inactivation of either gene would lead to a similar structural-variant signature. These associations between driver mutations and structural-variant signatures were consistently evident across many types of tumour (Extended Data Fig. 10).
The structural-variant signatures showed considerable heterogeneity in their activity across tumour types and among patients within a given tumour type ( Supplementary Fig. 8). Tumours of the gastrointestinal tract-including colorectal and oesophageal adenocarcinomas-showed high rates of the fragile-site signature. Prostate cancer was notable for the prevalence of the chromoplexy signature, as previously reported 5,20 , and squamous cell carcinomas of the lung were characterized by the fold-back inversion signature.
We assessed how classes of structural variant altered known cancer genes (Supplementary Table 1). Some cancer genes acquire oncogenic potential only with specific structural events, such as fusion genes or enhancer hijacking. Not surprisingly, these genes typically showed little variability in which classes of structural variant could generate such events (Extended Data Fig. 11a-c)-although there were exceptions. The TMPRSS2-ERG fusion gene of prostate cancer, for example, was generated by a range of processes (including simple deletions, chromoplexy and chromothripsis), all of which are prevalent signatures in this tumour type (Extended Data Fig. 11d-f).
Tumour-suppressor genes and recurrently amplified genes showed more variability in which types of structural variant were observed, and these were shaped by signatures active in the relevant tumour types. For example, the tumour-suppressor genes, PTEN and RAD51B, which are commonly inactivated in breast and ovarian cancers, were often targeted by tandem duplications generating out-of-frame exon duplications (Extended Data Fig. 12a, b). By contrast, deletions were the predominant events that inactivated SMAD4 and CDKN2A, in keeping with their prevalence in cancers of the gastrointestinal tract (Extended Data Fig. 12c, d). MYC, one of the most commonly amplified genes across all types of cancer, showed considerable diversity in the mechanisms of its rearrangement: nested tandem duplications in breast cancer, translocations or chromoplexy with IGH in lymphoma, as well as chromothripsis, cycles of templated insertions, local n-jumps and local-distant clusters in other types of tumour (Extended Data Fig. 13).

Discussion
We have described the patterns and signatures of structural variation in a large cohort of uniformly analysed cancer genomes. A major grouping of patterns in structural variants that emerges from our study is one in which extra copies of genomic templates are inserted during the rearrangement process. This includes simple events such as tandem duplications, as well as a range of more-complex events with duplications and triplications that are rearranged locally as well as inserted distantly. Our signature analysis grouped a large proportion of these more-complex events together with tandem duplications, which suggests that they represent a continuum of processes that share underlying properties. A replication-based mechanism has previously been proposed to explain local two-jumps 4,23,24 , in which stalled replication forks or other DNA lesions cause the DNA polymerase to switch templates and continue replication in a new location. Studies in experimental models are now revealing that a wide range of mechanisms and DNA lesions can result in templated insertions: these mechanisms include tandem duplications in BRCA1 deficiency 10 , translocations with templated insertions caused by dysregulated strand invasion 38 and distant templated insertions in the absence of replication helicases 39 .
Genomic instability in cancer is not a single phenomenon. Instead, many different mutational processes can act to restructure the genome and, in doing so, generate a notably flexible array of possible structures. Any given tumour draws on a subset of the available processes, shaped by the cell of origin, germline predisposition and other, unknown, factors: selection then does the rest, promoting the clone that has chanced on the structure that increases its potential for self-determination.

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14. Rheinbay, E. et al. Analyses of non-coding somatic drivers in 2,658 cancer whole genomes. Nature https://doi.org /10.1038/s41586-020-1965-x (2020  Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Methods
No statistical methods were used to predetermine sample size. The experiments were not randomized and investigators were not blinded to allocation during experiments and outcome assessment.
A detailed description of the methods used in this paper and many additional results are described in Supplementary Information. Here, we summarize the key aspects of the analysis.

Generation of the structural-variant call set
The final set of structural variants used in this Article was generated by the Technical Working Group of the PCAWG Consortium and is described in the main PCAWG paper 8 . In brief, four variant callers were used to identify somatically acquired structural variants from matched tumour and germline whole genome sequencing data: SvABA (Broad pipeline), DELLY (DKFZ pipeline), BRASS (Sanger pipeline) and dRanger (Broad pipeline). These were merged into a final call set using a graph-based algorithm to identify overlapping breakpoint junctions across algorithms. Detailed visual inspection of structural-variant calls suggested that a simple approach of accepting all structural-variant calls made by two or more of the four algorithms gave the best trade-off between sensitivity and specificity.

Structural-variant clustering and annotation
To identify clusters of structural variants, we developed a method for grouping structural variants into clusters and footprints to allow structural and mechanistic inferences to be made systematically. In parallel, we processed the somatic copy-number data and merged it with structural-variant junctions to enable us produce rearrangement patterns from the generated structural-variant clusters and footprints. We produced normalized representations of structuralvariant cluster patterns, which enable us to tabulate the number of different cluster and footprint patterns and analyse their features. Finally, we performed manual and simulation-assisted interpretation of the recurrently observed cluster and footprint patterns. The individual steps of the structural-variant classification pipeline are outlined below and detailed in the subsequent subsections: (1) computing the exact breakpoint coordinates from clipped reads; (2) removing redundant 'segment-bypassing' structural variants; (3) merging rearrangement breakpoints with copy-number data to yield structural-variant breakpoint-demarcated, normalized, absolute copy-number data; (4) clustering individual structural variants into structural-variant clusters and footprints; (5) heuristically refining structural-variant clusters and footprints; (6) filtering artefactual fold-back-type structural variants with insufficient support; (7) determining balanced overlapping breakpoints (this step is to distinguish very short templated insertions from mutually overlapping balanced breakpoints); and (8) computing rearrangement patterns and categories.

Distribution of structural variants across the genome
We divided the hg19 human reference genome (autosomes and chromosome X) into 3,036,315 pixels of 1 kb, and calculated a suite of metrics per pixel to summarize a variety of genome properties with potential relevance to the distribution of rearrangements, as listed in the Supplementary Information. Properties were matched as closely as possible to the tissue of origin for cancer samples from the PCAWG data. All other genome properties were held fixed across all tissues. To test for associations between structural-variant event classes and the library of genome properties, the genome property metrics were compared between real structural-variant positions (randomly choosing one side of each breakpoint junction to reduce dependence between observations) and one million uniform random positions from the callable genome space. To compare the tissue-specific properties, each random position was assigned a random tissue type, drawing from the observed tissue-type distribution in the structural-variant call set.
For each genome property and each event class, the real observations were pooled amongst the random ones, and then rank-transformed and normalized on a scale from 0 to 1. Under the null hypothesis of no event-versus-property association, the ranks of the real observations would follow a uniform distribution. We tested this in each case with a Kolmogorov-Smirnov test then applied a Benjamini-Yekutieli correction for false-discovery rate across the entire suite of tests and set the threshold for significance reporting at 0.01.

Structural-variant-signature analysis
We used two algorithms for extracting structural-variant signatures. Both used the same input files, comprising a matrix of counts per patient (across all patients) of structural-variant clusters falling into a number of mutually exclusive categories. These categories included the major classes of structural variants, with the more-common events (deletions, tandem duplications and inversions) split by size and/or replication timing. The two algorithms that were used for extracting the signatures were (1) a hierarchical Dirichlet process and (2) nonnegative matrix factorization. Further details on the implementation of these algorithms are available in the Supplementary Information.

Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this paper.

Data availability
Somatic and germline variant calls, mutational signatures, subclonal reconstructions, transcript abundance, splice calls and other core data generated by the ICGC/TCGA PCAWG Consortium are described in an accompanying Article 8 and are available for download at https://dcc. icgc.org/releases/PCAWG. Additional information on accessing the data, including raw read files, can be found at https://docs.icgc.org/ pcawg/data/. In accordance with the data access policies of the ICGC and TCGA projects, most molecular, clinical and specimen data are in an open tier that does not require access approval. To access information that could potentially identify participants, such as germline alleles and the underlying sequencing data, researchers will need to apply to the TCGA data access committee via dbGaP (https://dbgap.ncbi.nlm. nih.gov/aa/wga.cgi?page=login) for access to the TCGA portion of the dataset, and to the ICGC data access compliance office (http://icgc.org/ daco) for the ICGC portion of the dataset. In addition, to access somatic single-nucleotide variants derived from TCGA donors, researchers will also need to obtain dbGaP authorization.

Code availability
The core computational pipelines used by the PCAWG Consortium for alignment, quality control and variant calling are available to the public at https://dockstore.org/search?search=pcawg under the GNU General Public License v.3.0, which allows for reuse and distribution. These are described in detail in an accompanying Article 8 . The code for grouping structural variants into structural-variant clusters and footprints is available at https://github.com/cancerit/ClusterSV/ (version 1.0). The code for simulating rearrangements can be found at https://github.com/cancerit/SimSvGenomes (version 1.0). The code for sampling from the hierarchical Dirichlet process for identification of mutational signatures is implemented as an R package at https:// github.com/nicolaroberts/hdp (version 0.1.1).      Associations between a subset of the genomic properties (rows) and classes of structural variant (columns). Each density curve represents the quantile distribution of the genomic property values at observed breakpoints, compared to random genome positions. Asterisks indicate significant departures from uniform quantiles after multiple hypothesis correction by the Benjamini-Yekutieli method on a one-sided Kolmogorov-Smirnov test, based on a sample size of 2,559 genomes containing structural variants: *false-discovery rate < 0.01, **false-discovery rate < 0.001, ***false-discovery rate < 10 −6 . Cells with significant property associations are shaded by the magnitude of the shift of the median observed quantile above (blue) or below (red) 0.5. The interpretation of each property from left to right is indicated by the axes to the right of the property label.

Term Description
Structural variant (SV) Juxtaposition of non-contiguous chromosomal segments through a process of genomic rearrangement.

Breakpoint
The chromosomal position at which a DNA break is made. Each SV consists of a junction between two breakpoints in different regions of the genome.

Copy number alteration (CNA)
Change in the number of copies of a given chromosomal segment from that expected.

Reciprocal or balanced SV
A pair of SVs in which both sides of a single dsDNA break are rescued in the rearrangement. Typically used to describe some inversions and some translocations.
Unbalanced SV An SV (usually inversion or translocation) in which only one side of the dsDNA break is rescued, thereby generating a copy number alteration across the breakpoint.
Cluster of SVs A set of SVs that are closer together in genomic space than expected by chance. Typically, such clustering implies a shared mechanistic basis for the SV generation.

Derivative chromosome
A chromosome that carries one or more SVs.
Phased SVs Set of SVs and copy number alterations in a cluster carried on a single derivative chromosome.

Chromosomal segment
A contiguous stretch of DNA that is of constant copy number, used to denote the regions of chromosome between SVs.
Template A region of chromosomal DNA that is copied and inserted elsewhere in the genome.

SV class
A type of structural variant, such as deletion, tandem duplication or translocation.

Deletion
Loss of a segment of chromosome from the genome spanned by a junction between the two breakpoints either side.
Tandem duplication Extra copy of a segment of chromosome in which the duplicated region is inserted immediately adjacent to the original template in the same orientation.
Reciprocal inversion A segment of chromosomal DNA inserted into its original position, but in the opposite orientation.
Fold-back inversion An inverted rearrangement between two breakpoints typically <20kb apart on the chromosome, with associated copy number change. Often a sign of breakage-fusionbridge cycles.

Translocation
Breakpoint junction between two different chromosomes, either reciprocal or unbalanced.
Breakage-fusionbridge cycle SV mechanism in which a naked DNA end (breakage) is copied to its sister chromatid during S phase, with the two ends undergoing fusion (by fold-back inversion). At anaphase, the resulting dicentric chromosome is stretched between the two daughter cells (bridge), leading to further DNA breakage and potentially further cycles.
Chromoplexy A set of >2 reciprocal SVs in which the chromosomal ends either side of each breakpoint are shuffled such that every end is rescued in a rearrangement junction.

Chromothripsis
A cluster of many SVs (10s to 100s) in one or a few chromosomes, occurring in a single catastrophic event, with oscillating copy number profile and rearrangement junctions of all four possible orientations.
Local n-jump A cluster of n SVs in a single genomic region, typically phased to a single derivative chromosome, exhibiting some copy number gains and junctions with inverted and noninverted orientation.
Cycle, chain or bridge of templated insertions Copies of one or more genomic templates drawn from across the genome, strung together in a contiguous string and inserted into a single derivative chromosome. A chain of templated insertions does not return to the original chromosome, leading to an unbalanced translocation. A cycle has a duplication on the host chromosome, while a bridge inserts the template copies into a deletion on the host chromosome.
Local-distant cluster A cluster of SVs that has both local rearrangements and rearrangements to other parts of the genome.