Author Correction: The repertoire of mutational signatures in human cancer

Somatic mutations in cancer genomes are caused by multiple mutational processes, each of which generates a characteristic mutational signature1. Here, as part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium2 of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA), we characterized mutational signatures using 84,729,690 somatic mutations from 4,645 whole-genome and 19,184 exome sequences that encompass most types of cancer. We identified 49 single-base-substitution, 11 doublet-base-substitution, 4 clustered-base-substitution and 17 small insertion-and-deletion signatures. The substantial size of our dataset, compared with previous analyses3–15, enabled the discovery of new signatures, the separation of overlapping signatures and the decomposition of signatures into components that may represent associated—but distinct—DNA damage, repair and/or replication mechanisms. By estimating the contribution of each signature to the mutational catalogues of individual cancer genomes, we revealed associations of signatures to exogenous or endogenous exposures, as well as to defective DNA-maintenance processes. However, many signatures are of unknown cause. This analysis provides a systematic perspective on the repertoire of mutational processes that contribute to the development of human cancer. The characterization of 4,645 whole-genome and 19,184 exome sequences, covering most types of cancer, identifies 81 single-base substitution, doublet-base substitution and small-insertion-and-deletion mutational signatures, providing a systematic overview of the mutational processes that contribute to cancer development.

Somatic mutations in cancer genomes are caused by mutational processes of both exogenous and endogenous origin that operate during the cell lineage between the fertilized egg and the cancer cell 16 . Each mutational process may involve components of DNA damage or modification, DNA repair and DNA replication (which may be normal or abnormal), and generates a characteristic mutational signature that potentially includes base substitutions, small insertions and deletions (indels), genome rearrangements and chromosome copy-number changes 1 . The mutations in an individual cancer genome may have been generated by multiple mutational processes, and thus incorporate multiple superimposed mutational signatures. Therefore, to systematically characterize the mutational processes that contribute to cancer, mathematical methods have previously been used to decipher mutational signatures from somatic mutation catalogues, estimate the number of mutations that are attributable to each signature in individual samples and annotate each mutation class in each tumour with the probability that it arose from each signature 6,9,[17][18][19][20][21][22][23][24][25][26][27] .
Mutational signature analysis has predominantly used cancer exome sequences. However, the many-fold-greater numbers of somatic mutations in whole genomes provide substantially increased power for signature decomposition, enabling the better separation of partially correlated signatures and the extraction of signatures that contribute relatively small numbers of mutations. Furthermore, technical artefacts and differences in sequencing technologies and mutation-calling algorithms can themselves generate mutational signatures. Therefore, the uniformly processed and highly curated sets of all classes of somatic mutations from the 2,780 cancer genomes of the PCAWG project 2 , combined with most other suitable cancer genomes (accession code syn11801889, available at https://www.synapse.org/#!Synapse:syn11801889), present a notable opportunity to establish the repertoire of mutational signatures and determine their activities across different types of cancer. The timing of these signatures during the evolution of individual cancers and the repertoire of signatures of structural variation have been explored in other PCAWG analyses 30,34 .

Mutational signature analysis
The 23,829 samples-which include most types of cancer, and comprise the 2,780 PCAWG whole genomes 2 , 1,865 additional whole genomes and 19,184 exomes-yielded 79,793,266 somatic SBSs, 814,191 doublet-base substitutions (DBSs) and 4,122,233 small indels that were analysed for mutational signatures, about 10-fold-more mutations than any previous study of which we are aware (syn11801889) 6 .
We developed classifications for each type of mutation. For SBSs, the primary classification comprised 96 classes (available at https://cancer. sanger.ac.uk/cosmic/signatures/SBS) constituted by the 6 base substitutions C>A, C>G, C>T, T>A, T>C and T>G (in which the mutated base is represented by the pyrimidine of the base pair), plus the flanking 5′ and 3′ bases. In some analyses, two flanking bases 5′ and 3′ to the mutated base were considered (producing 1,536 classes) or mutations within transcribed genome regions were selected and classified according to whether the mutated pyrimidine fell on the transcribed or untranscribed strand (producing 192 classes). We also derived a classification for DBSs (78 classes; available at https://cancer.sanger.ac.uk/cosmic/signatures/ DBS). Indels were classified as deletions or insertions and-when of a single base-as C or T, and according to the length of the mononucleotide repeat tract in which they occurred. Longer indels were classified as occurring at repeats or with overlapping microhomology at deletion boundaries, and according to the size of indel, repeat and microhomology (83 classes; available at https://cancer.sanger.ac.uk/cosmic/signatures/ID).
The PCAWG whole-genome sequences, the additional whole-genome sequences and the exome sequences were each analysed separately (syn11801889) 2 . Signatures were extracted from each type of cancer individually, from all cancer types together, as separate SBS, DBS and indel signatures, and as composite signatures of all three types of mutation (Supplementary Note 2).
We used two methods based on nonnegative matrix factorization (NMF): SigProfiler, an elaborated version of the framework used for the previous 'Catalogue Of Somatic Mutations In Cancer' (COSMIC) compendium of mutational signatures (COSMIC v.2, available at https:// cancer.sanger.ac.uk/cosmic/signatures_v2) 11,17 , and SignatureAnalyzer, which is based on a Bayesian variant of NMF 9,27,35 . NMF determines the signature profiles and contributions of each signature to each cancer genome as part of its factorization of the input matrix of mutation spectra. However, with many signatures and/or heterogeneous mutation burdens across samples, the mutations observed in a particular sample can be reconstructed in multiple ways-often with small and/or biologically implausible contributions from many signatures. Therefore, each method has developed a separate procedure for estimating the contributions of signatures to each sample (Methods).
We tested SignatureAnalyzer and SigProfiler on 11 sets of synthetic data (including 64,400 synthetic samples), generated from known signature profiles (Methods, Supplementary Note 2). Both methods performed well in re-extracting known signatures from realistically complex data. Extracted signatures that were discordant from the known input usually arose from difficulties in selecting the correct number of signatures. The results confirm that use of NMF-based approaches for extracting mutational signatures is not a purely algorithmic process, but also requires consideration of evidence from experimentally determined mutational signatures and the DNA damage and repair literature, prior evidence of biological plausibility and human-guided sensitivity analysis confirming that extractions from different groupings of tumours yield consistent results. We used these types of evidence and approaches in determining the signature profiles reported here. The findings are consistent with results regarding NMF, and the related areas of probabilistic topic modelling and latent Dirichlet allocation, in multiple problem domains 36,37 . It is widely understood that the choice of the number of latent variables (for our purposes, the number of mutational signatures) is rarely amenable to complete automation.
The results from our SigProfiler and SignatureAnalyzer analyses of cancer data exhibited many similarities, and we assigned the same identifiers to similar signatures extracted using the two methods (syn12016215). However, there were also noteworthy differences. The numbers of SBS signatures found in PCAWG tumours with a low mutation burden (94.4% of cases that contain 47% of mutations) were similar: 31 using SigProfiler and 35 using SignatureAnalyzer. However, the numbers of additional SBS signatures extracted from hypermutated PCAWG samples (5.6% of cases, containing 53% of mutations) were different: 13 using SigProfiler and 25 using SignatureAnalyzer. There were also differences in SBS signature profiles, including among signatures found in cases with a low mutation burden. The latter primarily involved relatively featureless ('flat') signatures, which are mathematically challenging to deconvolute. Finally, there were differences in signature attributions to individual samples. SignatureAnalyzer used more signatures to reconstruct the mutational profiles (Extended Data Fig. 1) (syn12169204 and syn12177011) and attributions to flat signatures were different (Extended Data Fig. 2a, b) (syn12169204). The DBS and indel signatures were generally similar between the two methods (Extended Data Fig. 2c, d).
The final reference mutational signatures were determined from the PCAWG set, supplemented by additional signatures from the other datasets (COSMIC, available at https://cancer.sanger.ac.uk/cosmic/ signatures). Each signature was allocated an identifier consistent with, and extending, the COSMIC v.2 annotation. Some previous signatures split into multiple constituent signatures: these were numbered as in the previous annotation, but with additional letter suffixes (for example, SBS17 was split into SBS17a and SBS17b). DNA sequencing and analysis artefacts also generate mutational signatures. We indicate which signatures are possible artefacts but do not present them below (full information is available at https://cancer.sanger.ac.uk/cosmic/ signatures). The results of both SignatureAnalyzer and SigProfiler were used throughout the study. However, for brevity and for continuity with the signature set previously displayed in COSMIC v.2-which has been widely used as a reference-SigProfiler results are outlined here, and SignatureAnalyzer results are provided in Extended Data Figs. 3, 4 and at syn11738307.

Single-base substitution signatures
There were substantial differences in the numbers of SBSs between samples (ranging from hundreds to millions) and between cancer types 38 (Fig. 1). In total, 67 SBS mutational signatures were extracted, of which 49 were considered likely to be of biological origin (Fig. 2 6 ) were confirmed; the median cosine similarity between the newly Article derived signatures and those on COSMIC v.2 was 0.95, excluding the 'split' signatures (discussed below). SBS25 was previously found in cell lines derived from Hodgkin lymphomas treated with chemotherapy, and no primary cancers of this type were available. The newly derived signatures showed much improved separation from each other and more-distinct signature profiles, as compared with COSMIC v.2 signatures (see 'Better separation compared to COSMIC v.2 signatures' in Supplementary Note 2 for more information).
Thirteen of the SBS signatures we extracted (excluding those due to signature splitting) represent newly identified and probably real signatures, not present in COSMIC v.2. Some were rare (SBS31, SBS32, SBS35, SBS36, SBS42 and SBS44). Others were more common, but contributed relatively few mutations and/or were similar to previously discovered signatures (SBS38, SBS39 and SBS40). Notably, SBS40 is a flat signature similar to SBS5. It contributes to multiple types of cancer, but its similarity to SBS5 renders the extent of this contribution uncertain. For some of the newly identified signatures, there were plausible underlying aetiologies (Fig. 3, Extended Data Figs. 4, 5): for SBS31 and SBS35, platinum compound chemotherapy 39 ; for SBS32, azathioprine therapy; for SBS36, inactivating germline or somatic mutations in MUTYH (which encodes a component of the base excision repair machinery) 40,41 ; for SBS38, additional effects of exposure to ultraviolet (UV) light; for SBS42, occupational exposure to haloalkanes 13 ; and for SBS44, defective DNA mismatch repair 42 .
Three previously characterized base substitution signatures (SBS7, SBS10 and SBS17) split into multiple constituent signatures (Fig. 2). Signature splitting probably reflects the existence of multiple distinct mutational processes initiated by the same exposure that have closelybut not perfectly-correlated activities. We previously regarded SBS7 as a single signature composed predominantly of C>T at CCN and TCN trinucleotides (the mutated base is underlined) together with many fewer T>N mutations. It was found in malignant melanomas and squamous skin carcinomas, and is probably due to the UV-light-induced formation of pyrimidine dimers, followed by translesion DNA synthesis by error-prone polymerases predominantly inserting A opposite to damaged cytosines. SBS7 has now been decomposed into four constituent signatures. SBS7a and SBS7b (consisting mainly of C>T at TCN and C>T at CCN, respectively) may reflect different pyrimidine-dimer photoproducts. SBS7c and SBS7d (consisting predominantly of T>A at NTT and T>C at NTT, respectively 43 ) may be due to low frequencies of the misincorporation of T and G opposite to thymines in pyrimidine dimers. The splitting of SBS10 and SBS17 is described at https://cancer. sanger.ac.uk/cosmic/signatures/SBS/.
Using the SBS classification of 1,536 mutation types, which uses the sequence context two bases 5′ and two bases 3′ to each mutated base, yielded signatures that are largely consistent with those based on substitutions in trinucleotide contexts. Notably, however, two forms of both SBS2 and SBS13 were extracted, one with mainly a pyrimidine and the other with mainly a purine at the −2 base (the second base 5′ to the mutated cytosine). These may represent the activities of the cytidine deaminases APOBEC3A and APOBEC3B, respectively 45 . If so, APOBEC3A accounts for many more mutations than APOBEC3B in cancers with high APOBEC activity. Other signatures showed nonrandom sequence contexts at +2 and −2 positions (for example, SBS17a, SBS17b and SBS9), but sequence context effects were generally much stronger for bases immediately 5′ and 3′ to mutated bases.
SBS signatures showed substantial variation in the numbers of cancer types and cancer samples in which they were found, and in the mutations attributed per cancer sample (Fig. 3). Almost all individual cancer samples exhibited multiple signatures, with a mode of three in  the PCAWG set (syn12169204). The assigned signatures reconstruct well the mutational spectra of the cancer samples (in PCAWG samples, the median cosine similarity was 0.97; 96.3% of samples with cosine similarity >0.90): Fig. 4 shows illustrative examples.
Some mutational processes generate base substitutions that cluster in small genomic regions. The limited numbers of such mutations may result in a failure to detect their signatures using standard methods. We therefore identified clustered mutations in each genome and analysed ID1  ID2  ID3  ID4   ID5  ID6  ID7  ID8   ID9  ID10  ID11  ID12   ID13  ID14  ID15   Article them separately (Methods). Four main clustered mutational signatures were identified (Fig. 2), as previously reported 4,27,32 . Two, which are found in multiple types of cancer, were similar to SBS2 and SBS13 (which have been attributed to APOBEC enzyme activity) and represent foci of kataegis 3,32,46 . Two further clustered signatures, one characterized by C>T and C>G mutations at (A or G)C(C or T) trinucleotides 47 and the other T>A and T>C mutations at (A or T)T(A or T), were found in lymphoid neoplasms; they probably represent the direct and indirect consequences of activation-induced cytidine deaminase mutagenesis and translesion DNA synthesis by error-prone polymerases (SBS84 and SBS85, respectively) 27 .
A signature similar to DBS2 contributed hundreds of mutations to liver cancers and tens of mutations to other types of cancer without evidence of exposure to tobacco smoke. A pattern resembling DBS2 also dominates DBSs in healthy mouse cells 50 . The nature of the mutational processes that underlie these signatures in human cancers that are unrelated to smoking, and in healthy mice, is unknown. However, in experimental systems, acetaldehyde exposure has been shown to generate a mutational signature characterized primarily by CC>AA mutations, and lower burdens of CC>AG and CC>AT mutations, together with C>A SBSs 48 . Acetaldehyde is an oxidation product of alcohol and a constituent of cigarette smoke. The role of acetaldehyde, and perhaps other aldehydes, in generating DBS2 merits further investigation 51 .
DBS3, DBS7, DBS8 and DBS10 showed hundreds to thousands of mutations in rare colorectal, stomach and oesophageal cancers, some of which showed evidence of defective DNA mismatch repair (DBS7 and DBS10) or polymerase epsilon exonuclease domain mutations (DBS3) that generate hypermutator phenotypes (Figs. 2, 3). DBS5 was found in cancers exposed to platinum chemotherapy, and is associated with SBS31 and SBS35.

Small insertion-and-deletion signatures
Indels were usually present at about 10% of the frequency of base substitutions (Fig. 1). There was substantial variation between cancer genomes in the number of indels, even when cancers with evidence of defective DNA mismatch repair were excluded. Overall, the numbers of deletions and insertions were similar, but there was variation between cancer types: some cancers showed more deletions and others more insertions of various subtypes (Fig. 1). We extracted 17 indel mutational signatures (Fig. 2).
Indel signature 1 (ID1) was composed predominantly of insertions of thymine and ID2 was composed predominantly of deletions of thymine, both at long (≥5) thymine mononucleotide repeats (Fig. 2). Tens to hundreds of mutations of both signatures were found in most samples of most types of cancer, but were particularly common in colorectal, stomach, endometrial and oesophageal cancers and in diffuse large B cell lymphoma (Fig. 3). Together, ID1 and ID2 accounted for 97% and 45% of indels in hypermutated and non-hypermutated cancer genomes, respectively (Extended Data Table 2). They are probably due to slippage of either the nascent (ID1) or template strand (ID2) during DNA replication of long mononucleotide tracts.
ID3 was characterized predominantly by deletions of cytosine at short (≤5-bp long) mononucleotide cytosine repeats and exhibited hundreds of mutations in cancers of the lung, head and neck that are associated with tobacco smoking (Figs. 2, 3). There was transcriptional strand bias of mutations, with more guanine deletions than cytosine deletions on the untranscribed strands of genes, which is compatible with transcription-coupled nucleotide excision repair of damaged guanine (syn12177065 and syn12177066). The numbers of ID3 mutations positively correlated with the numbers of SBS4 and DBS2 mutations, which we have shown are associated with tobacco smoking (Extended Data Figs. 6, 7). Thus, DNA damage by components of tobacco smoke probably underlie ID3.
ID13 was characterized predominantly by deletions of thymine at thymine-thymine dinucleotides and exhibited large numbers of mutations in malignant melanomas of the skin (Figs. 2, 3  Article at cytosine-cytosine dinucleotides did not feature strongly in ID13, which may reflect the predominance of thymine compared to cytosine dimers induced by UV light 52 . ID6 and ID8 were both characterized predominantly by ≥5-bp deletions (Fig. 2). ID6 exhibited overlapping microhomology at deletion boundaries with a mode of 2 bp (and often longer stretches) and correlated with SBS3, which we have attributed to defective homologousrecombination-based repair (Extended Data Figs. 6, 7). By contrast, ID8 deletions showed shorter or no microhomology at deletion boundaries and did not strongly correlate with SBS3. Both deletion patterns may be characteristic of DNA double-strand-break repair by non-homologousrecombination-based end-joining mechanisms and-if so-this suggests that at least two distinct forms are operative in human cancer 53 .
A small fraction of cancers exhibited very large numbers of ID1 and ID2 mutations (>10,000) ( Fig. 3) (shown at https://cancer.sanger.ac.uk/ cosmic/signatures/ID). These were usually accompanied by SBS6, SBS14, SBS15, SBS20, SBS21, SBS26 and/or SBS44, which are associated with deficiency in DNA mismatch repair-sometimes combined with POLE or POLD1 proofreading deficiency (SBS14 and SBS20) 35 . Occasional cases with these signatures additionally showed large numbers of indels attributed to ID7 (syn11738668), and rare samples showed large numbers of ID4, ID11, ID14, ID15, ID16 or ID17 mutations but did not show large numbers of ID1 and ID2 mutations or the SBS signatures associated with deficiency in DNA mismatch repair.

Correlations with age
A positive correlation between age of cancer diagnosis and the number of mutations attributable to a signature suggests that the underlying mutational process has been operative (at a more or less constant rate) throughout the cell lineage from fertilized egg to cancer cell, and thus in the normal cells from which that type of cancer develops 6,54 . Confirming previous reports 6, 54 , the numbers of SBS1 and SBS5 mutations correlate with age, and exhibit different rates in different types of tissue (q values provided in syn12030687, syn20317940 and syn12217988). SBS40 also correlated with age in multiple types of cancer, although-given its similarity to SBS5-misattribution cannot be excluded. DBS2 and DBS4 correlated with age; consistent with activity in normal cells and, when combined their profiles closely resemble the spectrum of DBS mutations found in normal mouse cells 50 . ID1, ID2, ID5 and ID8 showed correlations with age in multiple tissues. ID1 and ID2 indels are probably due to slippage at poly T repeats during DNA replication and correlated with the numbers of SBS1 substitutions, which have previously been proposed to reflect the number of mitoses a cell has experienced 6 . Thus, SBS1, ID1 and ID2 may all be generated during DNA replication at mitosis. The number of ID5 mutations correlated with the number of SBS40 mutations, and the mutational processes that underlie these two age-correlated signatures may therefore contain common components. ID8, which is predominantly composed of ≥5-bp deletions with no or 1 bp of microhomology at their boundaries, is probably due to DNA double-strand breaks repaired by a non-homologous-end-joining mechanism. The results indicate that multiple mutational processes operate in normal cells.

Discussion
There are important constraints, limitations and assumptions in the analytic frameworks used here to characterize mutational signatures. Signatures extracted from sample sets in which multiple processes are operative remain mathematical approximations, with profiles that are potentially influenced by the mathematical approach used and other factors. For conceptual and practical simplicity, we assume that a single signature is associated with each mutational process and provide an average reference signature to represent it. However, we do not discount the possibility that further nuances and variations of signature profiles exist. We have estimated the contributions from each signature to the mutation burden in each sample. However, with increasing numbers of signatures and differences of multiple orders of magnitude in mutation burdens between some signatures, prior knowledge has helped to avoid biologically implausible results. Thus, the further development of methods for deciphering and attributing mutational signatures is warranted, ideally supported by signatures derived from experimental systems in which the causes are known. Nevertheless, signatures with many similarities and some differences can be found by different mathematical approaches, and these can be confirmed in several ways, including experimentally elucidated signatures 5,31,39,42,43,[54][55][56][57][58][59][60][61][62] and tumours dominated by a single signature (syn12016215).
This analysis includes most publicly available exome and wholegenome cancer sequences. Some rare or geographically restricted signatures may not have been captured, signatures conferring limited mutation burdens may have been missed and signatures of therapeutic mutagenic exposures have not been exhaustively explored. Nevertheless, it is likely that a substantial proportion of the naturally occurring mutational signatures found in human cancer have now been described. This comprehensive repertoire provides a foundation for research into the aetiologies of geographical and temporal differences in cancer incidence, the mutational processes that operate in healthy tissues and non-neoplastic disease states, clinical and public health applications of signatures and mechanistic understanding of the mutational processes that underlie carcinogenesis.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-020-1943-3.

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.
These online methods contain an abridged description of the methodology used in the current manuscript; extensive details about the methodology we used are provided in Supplementary Note 2. Importantly, two independently developed computational frameworks (Sig-Profiler and SignatureAnalyzer) based on NMF were applied separately to the examined sets of mutational catalogues. SigProfiler and Signa-tureAnalyzer take different approaches for deciphering mutational signatures and for assigning each signature to each sample. By using two methods, we aimed to provide a perspective on the effect that different methodologies can have on the numbers of signatures generated, signature profiles and attributions. In addition to applying SigProfiler and SignatureAnalyzer to cancer data, the tools were also applied to realistic synthetic data with known solutions.

Analysis of mutational signatures with SigProfiler
SigProfiler incorporates two distinct steps for identification of mutational signatures, based on the previously described methodology 6,11,17 (Extended Data Fig. 8). The first step (SigProfilerExtraction) encompasses a hierarchical de novo extraction of mutational signatures based on somatic mutations and their immediate sequence context, and the second step (SigProfilerAttribution) focuses on accurately estimating the number of somatic mutations associated with each extracted mutational signature in each sample. SigProfilerExtraction is an extension of a previous framework for the analysis of mutational signatures 11,17 . In brief, for a given set of mutational catalogues, the algorithm deciphers a minimal set of mutational signatures that optimally explains the proportion of each mutation type and estimates the contribution of each signature to each sample. More specifically, for each NMF iteration, SigProfilerExtraction minimizes a generalized Kullback-Leibler divergence constrained for nonnegativity (Supplementary Note 2). The algorithm uses multiple NMF iterations (in most cases 1,024) to identify the matrix of mutational signatures and the matrix of the activities of these signatures, as previously described 17 . The unknown number of signatures is determined by human assessment of the stability and accuracy of solutions for a range of values, as previously described 17 . The framework is applied hierarchically to increase its ability to find mutational signatures that generate few mutations or are present in few samples.
After signatures are discovered by SigProfilerExtraction, SigPro-filerAttribution estimates their contributions to individual samples. For each examined sample, the estimation algorithm involves finding the minimum of the Frobenius norm of a constrained function using a nonlinear convex optimization programming solver using the interiorpoint algorithm 63 . See Supplementary Note 2 and Extended Data Fig.  8b for further details.

Analysis of mutational signatures with SignatureAnalyzer
SignatureAnalyzer uses a Bayesian variant of NMF that infers the number of signatures through the automatic relevance determination technique and delivers highly interpretable and sparse representations for both signature profiles and attributions that strike a balance between data fitting and model complexity. Further details of the actual implementation of the computational approach have previously been published 9,27,64 . SignatureAnalyzer was applied by using a two-step signature extraction strategy using 1,536 pentanucleotide contexts for SBSs, 83 indel features and 78 DBS features. In addition to the separate extraction of SBS, indel and DBS signatures, we performed a 'COMPOSITE' signature extraction based on all 1,697 features (1,536 SBS + 78 DBS + 83 indel). For SBSs, the 1,536 SBS COMPOSITE signatures are preferred; for DBSs and indels, the separately extracted signatures are preferred.
In step 1 of the two-step extraction process, global signature extraction was performed for the samples with a low mutation burden (n = 2,624). These excluded hypermutated tumours: those with putative polymerase epsilon (POLE) defects or mismatch repair defects (microsatellite instable tumours), skin tumours (which had intense UV-light mutagenesis) and one tumour with temozolomide (TMZ) exposure. Because the underlying algorithm of SignatureAnalyzer performs a stochastic search, different runs can produce different results. In step 1, we ran SignatureAnalyzer 10 times and selected the solution with the highest posterior probability. In step 2, additional signatures unique to hypermutated samples were extracted (again selecting the highest posterior probability over ten runs) while allowing all signatures found in the samples with low mutation burden, to explain some of the spectra of hypermutated samples. This approach was designed to minimize a well-known 'signature bleeding' effect or a bias of hyper-or ultramutated samples on the signature extraction. In addition, this approach provided information about which signatures are unique to the hypermutated samples, which was later used when attributing signatures to samples.
A similar strategy was used for signature attribution: we performed a separate attribution process for low-and hypermutated samples in all COMPOSITE, SBS, DBS and indel signatures. For downstream analyses, we preferred to use the COMPOSITE attributions for SBSs and the separately calculated attributions for DBSs and indels. Signature attribution in samples with a low mutation burden was performed separately in each tumour type (for example, Biliary-AdenoCA, Bladder-TCC, Bone-Osteosarc, and so on). Attribution was also performed separately in the combined microsatellite instable tumours (n = 39), POLE (n = 9), skin melanoma (n = 107) and TMZ-exposed samples (syn11738314). In both groups, signature availability (which signatures were active, or not) was primarily inferred through the automatic relevance determination process applied to the activity matrix H only, while fixing the signature matrix W. The attribution in samples with a low mutation burden was performed using only signatures found in the step 1 of the signature extraction. Two additional rules were applied in SBS signature attribution to enforce biological plausibility and minimize a signature bleeding: (i) allow SBS4 (smoking signature) only in lung, head and neck cases; and (ii) allow SBS11 (TMZ signature) in a single GBM sample. This was enforced by introducing a binary, signature-by-sample signature indicator matrix Z (1, allowed; 0, not allowed), which was multiplied by the H matrix in every multiplication update of H. No additional rules were applied to indel or DBS signature attributions, except that signatures found in hypermutated samples were not allowed in samples with a low mutation burden.

Application of SigProfiler and SignatureAnalyzer to synthetic data
Our goal was to evaluate SignatureAnalyzer and SigProfiler on realistic synthetic data to identify any potential limitations of these two methods. SignatureAnalyzer and SigProfiler were tested on 11 sets of synthetic data, encompassing a total of 64,400 synthetic samples, in which known signature profiles were used to generate catalogues of synthetic mutational spectra. We operationally defined 'realistic' data as those based on the characteristics of either SignatureAnalyzer's or SigProfiler's analysis of the PCAWG genome data. SignatureAnalyzer's reference signature profiles were based on COMPOSITE signatures, consisting of 1,536 types of strand-agnostic SBSs in pentanucleotide context, 78 types of DBSs and 83 types of small indels, for a total of 1,697 mutation types. SigProfiler's reference analysis was based on strand-agnostic SBSs in the context of one 5′ and one 3′ base. For each test, we generated two sets of realistic data: SigProfiler-realistic (based on SigProfiler's reference signatures and attributions) and Signature-Analyzer-realistic (based on SignatureAnalyzer's reference signatures and attributions), as well as two other types of data that involved using SignatureAnalyzer profiles with SigProfiler attributions and vice versa.
A detailed description of each of the 11 sets of synthetic data and the results from applying SigProfiler and SignatureAnalyzer are provided in Supplementary Note 2.

Analysis of clustered mutational signatures
Somatic SBSs were considered clustered if they had intermutational distances < 1,000 bp. More specifically, for each sample, an SBS mutational catalogue was generated for substitutions that were <1,000 bp from another substitution. Subsequently, the set of SBS mutational catalogues containing clustered mutations underwent de novo extraction of mutational signatures. Any novel mutational signature (one that was not previously observed in the complete SBS catalogues) was reported as a clustered mutational signature.
Better separation compared to COSMIC v.2 signatures As described in the manuscript, all mutational signatures previously reported in COSMIC v.2 were confirmed in the new set of analyses with median cosine similarity of 0.95. However, the separation between the COSMIC v.2 mutational signatures (https://cancer.sanger.ac.uk/ cosmic/signatures_v2) is much worse than the separation between the mutational signatures reported here. For example, in COSMIC v.2, signatures 5 and 16 had a cosine similarity of 0.90, making them hard to distinguish from one another. By contrast, in the current analysis, SBS5 and SBS16 have a cosine similarity of 0.65. This allows us to unambiguously assign SBS5 and SBS16 to different samples. In the current analysis, the larger number of samples has allowed the reduction of bleeding between signatures and has given more unique and easily distinguishable signatures. One can evaluate the overall separation of a set of mutational signatures by examining the distribution of cosine similarities between the signatures in the set. The signatures in COS-MIC v.2 had a median cosine similarity of 0.238. By contrast, the current signatures have a much lower median cosine similarity of 0.098. This twofold reduction in similarity is highly statistically significant (P value 9.1 × 10 −25 ) and indicates a better separation between the signatures in the current analysis.

Correlations of mutational signature activity with age
Before evaluating the association between age and the activity of a mutational signature, all outliers for both age and numbers of mutations attributed to a signature in a cancer type were removed from the data. An outlier was defined as any value outside three standard deviations from the mean value. A robust linear regression model that estimated the slope of the line and whether this slope was significantly different from zero (F test; P value < 0.05) was performed using the MATLAB function robustfit (https://www.mathworks.com/help/stats/ robustfit.html) with default parameters. The P values from the F tests were corrected using the Benjamini-Hochberg procedure for false discovery rates. Results are available at syn12030687 and syn20317940.

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 and TCGA PCAWG Consortium are described in ref. 2 , 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. For each mutational signature as extracted by SigProfiler, there is a 'vignette' that consists of plots and a short textual description at COSMIC (available at https://cancer.sanger.ac.uk/cosmic/signatures/). Beyond the core sequence data generated by the ICGC and TCGA PCAWG Consortium, other derived datasets were generated by the research reported in this paper. These derived datasets are available at Synapse (https://www. synapse.org/#!Synapse:syn11726601/wiki/513478), and are denoted by accession numbers (synXXXXXXXX). All these datasets are mirrored at https://dcc.icgc.org/releases/PCAWG/mutational_signatures/ with full links, filenames, accession numbers and descriptions as detailed in Supplementary Table 1. These datasets include (1) CSV files comprising all catalogues of observed mutational spectra that were used as input to signature extraction (syn11801889), (2) CSV files and plots of signatures extracted by SigProfiler (syn11738306) and SignatureAnalyzer (syn11738307), (3) CSV files with estimates of the numbers of mutations generated by each signature in individual tumours (syn11804065), (4) estimates of the probability that each signature was responsible for each mutational type (for example, CTG>CAG) in individual tumours (syn11804068) and (5)   Extended Data Fig. 8

| SigProfiler signature extraction and attribution.
A full description is provided in Supplementary Note 2. a, Procedure for extracting (discovering) mutational signatures.
Step A, apply the approach to a set of samples D; initially D contains all samples (that is, D = M). This step has previously been described in detail 17 .
Step B, solution evaluation and reiteration. Extracted mutational signatures and their activities in individual samples are saved into a set (S). The activity of any signature that does not increase the cosine similarity of a sample by > 0.01 was removed from the sample (assigned a value of 0).
Step A is repeated for all samples for which the identified signatures do not explain their patterns (cosine similarity < 0.95). The algorithm continues to step C when step A cannot find any stable signatures. Step

Statistics
For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.

n/a Confirmed
The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one-or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.
A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable.

For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings
For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above.

Software and code
Policy information about availability of computer code
For the larger PCAWG Consortium, data and metadata were collected from International Cancer Genome Consortium (ICGC) consortium members using custom software packages designed by the ICGC Data Coordinating Centre. The general-purpose core libraries and utilities underlying this software have been released under the GPLv3 open source license as the "Overture" package and are available at https://www.overture.bio. Other data collection software used in this effort, such as ICGC-specific portal user interfaces, are available upon request to contact@overture.bio.

Data analysis
SigProfiler is available both as a MATLAB framework and as a Python package.

Life sciences study design
All studies must disclose on these points even when the disclosure is negative.

Sample size
From a statistical perspective this was an exploratory study, and there were no pre-defined hypothesis tests for which sample-size power calculations would have been appropriate. The sample size was determined by numbers of tumour genomes and exomes represented by publicly available somatic mutation data. These data consisted of the ICGC Pan Cancer whole genome mutation data, the TCGA MC3 whole exome mutation data, and additional mutation data as described in https://www.synapse.org/#!Synapse:syn11801788. This was an unsupervised analysis, and therefore we extracted as many signatures as possible from all the available data. This enabled a substantial increment over previously available sets of mutational signatures, especially with respect to double base substitution (DBS) signatures and insertion/deletion (ID) signatures.
For the larger PCAWG Consortium, the Consortium compiled an inventory of matched tumour/normal whole cancer genomes in the ICGC Data Coordinating Centre. Most samples came from treatment-naïve, primary cancers, but there were a small number of donors with multiple samples of primary, metastatic and/or recurrent tumours. Our inclusion criteria were: (i) matched tumour and normal specimen pair; (ii) a minimal set of clinical fields; and (iii) characterisation of tumour and normal whole genomes using Illumina HiSeq paired-end sequencing reads. We collected genome data from 2,834 donors, representing all ICGC and TCGA donors that met these criteria at the time of the final data freeze in autumn 2014.
Data exclusions From a statistical perspective this was an exploratory study, and there were no pre-defined hypothesis tests for which pre-defined data exclusion criteria would have been appropriate. Therefore, no data were excluded from analysis by our algorithms.
For the larger PCAWG Consortium, after quality assurance, data from 176 donors were excluded as unusable. Reasons for data exclusions included inadequate coverage, extreme bias in coverage across the genome, evidence for contamination in samples and excessive sequencing errors (for example, through 8-oxoguanine).

Replication
This was not an experimental study, and there were no experimental replicates.
For the larger PCAWG Consortium, in order to evaluate the performance of each of the mutation-calling pipelines and determine an integration strategy, we performed a large-scale deep sequencing validation experiment. We selected a pilot set of 63 representative tumour/ normal pairs, on which we ran the three core pipelines, together with a set of 10 additional somatic variant-calling pipelines contributed by members of the SNV Calling Working Group. Overall, the sensitivity and precision of the consensus somatic variant calls were 95% (CI90%: 88-98%) and 95% (CI90%: 71-99%) respectively for SNVs. For somatic indels, sensitivity and precision were 60% (34-72%) and 91% (73-96%) respectively. Regarding SVs, we estimate the sensitivity of the merging algorithm to be 90% for true calls generated by any one caller; precision was estimated as 97.5% -that is, 97.5% of SVs in the merged SV call-set have an associated copy number change or balanced partner rearrangement.
Randomization There were no experimental groups in this study; the question of allocation to experimental groups is not applicable.
For the larger PCAWG Consortium, no randomisation was performed.

October 2018
Blinding There was no allocation to experimental groups; the question of whether investigators were blinded to allocation is not applicable.
For larger PCAWG Consortium, no blinding was undertaken.

Behavioural & social sciences study design
All studies must disclose on these points even when the disclosure is negative.

Ethics oversight
Identify the organization(s) that approved or provided guidance on the study protocol, OR state that no ethical approval or guidance was required and explain why not.
Note that full information on the approval of the study protocol must also be provided in the manuscript.

Human research participants
Policy information about studies involving human research participants

Population characteristics
For the PCAWG Consortium data, patient-by-patient clinical data are provided in the marker paper for the PCAWG consortium (Extended Data Table 1 of that manuscript). Demographically, the cohort included 1,469 males (55%) and 1,189 females (45%), with a mean age of 56 years (range, 1-90 years). Using population ancestry-differentiated single nucleotide polymorphisms (SNPs), the ancestry distribution was heavily weighted towards donors of European descent (77% of total) followed by East Asians (16%), as expected for large contributions from European, North American and Australian projects. We consolidated histopathology descriptions of the tumour samples, using the ICD-0-3 tumour site controlled vocabulary. Overall, the PCAWG data set comprises 38 distinct tumour types. While the most common tumour types are included in the dataset, their distribution does not match the relative population incidences, largely due to differences among contributing ICGC/TCGA groups in numbers sequenced. The non-PCAWG analyses used previously published data.

Recruitment
For the PCAWG Consortium data, patients were recruited by the participating centres following local protocols.

Ethics oversight
For the PCAWG Consortium data, the Ethics oversight for the PCAWG protocol was undertaken by the TCGA Program Office and the Ethics and Governance Committee of the ICGC. Each individual ICGC and TCGA project that contributed data to PCAWG had their own local arrangements for ethics oversight and regulatory alignment.
Note that full information on the approval of the study protocol must also be provided in the manuscript.

Clinical data
Policy information about clinical studies All manuscripts should comply with the ICMJE guidelines for publication of clinical research and a completed CONSORT checklist must be included with all submissions.

Clinical trial registration
Provide the trial registration number from ClinicalTrials.gov or an equivalent agency.

Study protocol
Note where the full trial protocol can be accessed OR if not available, explain why.

Data collection
Describe the settings and locales of data collection, noting the time periods of recruitment and data collection.

Outcomes
Describe how you pre-defined primary and secondary outcome measures and how you assessed these measures.

ChIP-seq Data deposition
Confirm that both raw and final processed data have been deposited in a public database such as GEO.
Confirm that you have deposited or provided access to graph files (e.g. BED files) for the called peaks.

Data access links
May remain private before publication.
For "Initial submission" or "Revised version" documents, provide reviewer access links. For your "Final submission" document, provide a link to the deposited data.

Files in database submission
Provide a list of all files available in the database submission.
Genome browser session (e.g. UCSC) Provide a link to an anonymized genome browser session for "Initial submission" and "Revised version" documents only, to enable peer review. Write "no longer applicable" for "Final submission" documents. 6 nature research | reporting summary October 2018

Methodology Replicates
Describe the experimental replicates, specifying number, type and replicate agreement.

Sequencing depth
Describe the sequencing depth for each experiment, providing the total number of reads, uniquely mapped reads, length of reads and whether they were paired-or single-end.

Antibodies
Describe the antibodies used for the ChIP-seq experiments; as applicable, provide supplier name, catalog number, clone name, and lot number.

Peak calling parameters
Specify the command line program and parameters used for read mapping and peak calling, including the ChIP, control and index files used.

Data quality
Describe the methods used to ensure data quality in full detail, including how many peaks are at FDR 5% and above 5-fold enrichment.

Software
Describe the software used to collect and analyze the ChIP-seq data. For custom code that has been deposited into a community repository, provide accession details.

Flow Cytometry
Plots Confirm that: The axis labels state the marker and fluorochrome used (e.g. CD4-FITC).
The axis scales are clearly visible. Include numbers along axes only for bottom left plot of group (a 'group' is an analysis of identical markers).
All plots are contour plots with outliers or pseudocolor plots.
A numerical value for number of cells or percentage (with statistics) is provided.

Methodology Sample preparation
Describe the sample preparation, detailing the biological source of the cells and any tissue processing steps used.

Instrument
Identify the instrument used for data collection, specifying make and model number.

Software
Describe the software used to collect and analyze the flow cytometry data. For custom code that has been deposited into a community repository, provide accession details.
Cell population abundance Describe the abundance of the relevant cell populations within post-sort fractions, providing details on the purity of the samples and how it was determined.

Gating strategy
Describe the gating strategy used for all relevant experiments, specifying the preliminary FSC/SSC gates of the starting cell population, indicating where boundaries between "positive" and "negative" staining cell populations are defined.
Tick this box to confirm that a figure exemplifying the gating strategy is provided in the Supplementary Information.

Magnetic resonance imaging
Experimental design Design type Indicate task or resting state; event-related or block design.

Specify the number of blocks, trials or experimental units per session and/or subject, and specify the length of each trial or block (if trials are blocked) and interval between trials.
Behavioral performance measures State number and/or type of variables recorded (e.g. correct button press, response time) and what statistics were used to establish that the subjects were performing the task as expected (e.g. mean, range, and/or standard deviation across subjects).