Cancer develops through a continuous process of somatic evolution. Whole genome sequencing provides a snapshot of the tumor genome at the point of sampling, however, the data can contain information that permits the reconstruction of a tumor9s evolutionary past. Here, we apply such life history analyses on an unprecedented scale, to a set of 2,658 tumors spanning 39 cancer types. We estimated the timing of large chromosomal gains during tumor evolution, by comparing the rates of doubled to non-doubled point mutations within gained regions. Although we find that such events typically occur in the second half of clonal evolution, we also observe distinctive and early chromosomal gains in some cancer types, such as gains of chromosomes 7, 19 and 20 in glioblastoma, and isochromosome 17q in medulloblastoma. By integrating these results with the qualitative timing of individual driver mutations, we obtained an overall ranking, from early to late, of frequent somatic events per cancer type, which both identified novel patterns of tumor evolution, and incorporated additional detail into known models, such as the progression of APC-KRAS-TP53 in colorectal cancer proposed by Vogelstein and Fearon. To estimate how mutational processes acting on the tumor genome change over time, we classified mutations in each sample according to three broad time periods (early clonal, late clonal, and subclonal), and quantified the activity of mutational signatures in each period. Most mutational processes appear to remain remarkably constant, however, certain signatures show clear and consistent changes during clonal evolution. Particularly, mutational signatures associated with exposure to carcinogens, such as smoking and UV light, tend to decrease over time. In contrast, signatures associated with defective endogenous processes, such as APOBEC mutagenesis and defective double strand break repair, show an increase between early and late phases of tumor evolution. Making use of clock-like mutational signatures, we converted mutational time estimates for large events, such as whole genome duplication (WGD), and the emergence of the most recent common ancestor (MRCA), into real time estimates, which allowed us to combine our analyses into overall timelines of cancer evolution, per tumor type. For example, the typical timeline of ovarian adenocarcinoma development shows that early tumor evolution is characterized by mutations in TP53, and widespread genome instability, with WGD events taking place on average 8 years prior to diagnosis. In later stages of evolution, signatures of defective repair processes increase, and the MRCA emerges on average 1 year before diagnosis. Taken together, these data reveal the common and divergent evolutionary trajectories available to a cancer, which might be crucial in understanding specific tumor biology, and in providing new opportunities for early detection and cancer prevention. Citation Format: Clemency Jolly, Moritz Gerstung, Ignaty Leshchiner, Stefan C. Dentro, Santiago Gonzalez, Thomas J. Mitchell, Yulia Rubanova, Pavana Anur, Daniel Rosebrock, Kaixian Yu, Maxime Tarabichi, Amit Deshwar, Jeff Wintersinger, Kortine Kleinheinz, Ignacio Vasquez-Garcia, Kerstin Haase, Subhajit Sengupta, Geoff Macintyre, Salem Malikic, Nilgun Donmez, Dimitri G. Livitz, Mark Cmero, Jonas Demeulemeester, Steve Schumacher, Yu Fan, Xiaotong Yao, Juhee Lee, Matthias Schlesner, Paul C. Boutros, David D. Bowtell, Hongtu Zhu, Gad Getz, Marcin Imielinski, Rameen Beroukhim, S Cenk Sahinalp, Yuan Ji, Martin Peifer, Florian Markowetz, Ville Mustonen, Ke Juan, Wenyi Wang, Quaid D. Morris, Paul T. Spellman, David C. Wedge, Peter Van Loo, PCAWG Evolution and Heterogeneity Working Group. The evolutionary history of 2,658 cancers [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 218.

We have characterised intra-tumour heterogeneity (ITH) across 2,778 whole genome sequences of tumours in the International Cancer Genome Consortium Pan-Cancer Analysis of Whole Genomes project, representing 36 distinct cancer types. We applied 6 copy number (CNA) callers and 11 subclonal reconstruction algorithms and developed approaches to integrate the results in robust, high-confidence CNA calls and subclonal architectures. The analysis reveals widespread ITH. We find at least one subclone in nearly all (96.7%) tumours with sufficient sequencing depth. Analysis using dN/dS ratios yields clear signs of positive selection in clonal and subclonal mutations and we find subclonal driver mutations in known driver genes. However, only 24% of subclones contain a driver mutation in a known driver gene, suggesting that a multitude of undiscovered late drivers exist and that tumours continue to undergo selection after tumourigenesis, at least until diagnosis. Consistent with other studies, we find that in 9% of tumours all clinically actionable mutations are subclonal, while 20% of tumours contain at least one subclonal actionable driver. These findings emphasise the relevance of ITH in treatment decision making. Distinct patterns of ITH emerge; for example, prostate, uterus and esophageal adenocarcinomas show high proportions of both subclonal single nucleotide variants (SNVs) and CNAs. Kidney chromophobe and pancreatic endocrine tumours also contain high proportions of subclonal SNVs, but few subclonal CNAs. On the other hand, hepatocellular carcinomas and head-and-neck and lung SCCs contain low proportions of subclonal SNVs and high proportions of subclonal CNAs. Mutational signature analysis reveals changes in signature activity. Exposures to UV light in melanomas and acid reflux in stomach and oesophageal cancers contribute more clonal mutations. While APOBEC and DNA damage repair response related signatures show increased activity in subclones. These findings highlight distinct evolutionary narratives between and within histologically distinct tumour types. Citation Format: Stefan Dentro, Ignaty Leshchiner, Kerstin Haase, Jeff Wintersinger, Amit Deshwar, Maxime Tarabichi, Yulia Rubanova, Kaixian Yu, Ignacio Vazquez Garcia, Geoff Macintyre, Kortine Kleinheinz, Dimitri Livitz, Salem Malikic, Nilgun Donmez, Subhajit Sengupta, Yuan Ji, Jonas Demeulemeester, Pavana Anur, Clemency Jolly, Marek Cmero, Daniel Rosebrock, Steve Schumacher, Yu Fan, Matthew Fittall, Xiaotong Yao, Juhee Lee, Matthias Schlesner, Hongtu Zhu, David Adams, Gad Getz, Paul Boutros, Marcin Imielinski, Rameen Beroukhim, Cenk Sahinalp, Martin Peifer, Inigo Martincorena, Florian Markowetz, Ville Mustonen, Ke Yuan, Moritz Gerstung, Wenyi Wang, Paul Spellman, Quaid Morris, David Wedge, Peter Van Loo. Pervasive intra-tumour heterogeneity and subclonal selection across cancer types [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 3000.

Ongoing cancer evolution gives rise to intra-tumour heterogeneity (ITH), which is a major mechanism of therapeutic resistance and therefore an important clinical challenge. However, the extent, origin and drivers of ITH across cancer types are poorly understood. Here, we extensively characterise ITH across 2,778 cancer whole genome sequences from 36 cancer types. We demonstrate that nearly all tumours (94.7%) with sufficient sequencing depth contain evidence of recent subclonal expansions, and that most cancer types show clear signs of positive selection in both clonal and subclonal protein coding variants. We find distinctive subclonal patterns of driver gene mutations, fusions, structural variation and copy-number alterations across cancer types. Dynamic, tumour type-specific changes of mutational processes between subclonal expansions shape differences between clonal and subclonal events. Our results underline the importance of ITH and its drivers in tumour evolution, and provide an unprecedented pan-cancer resource of extensively annotated subclonal events, laying a foundation for future cancer genomic studies.

We introduce a new edit distance measure between a pair of "clonal trees", each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree edit distance (MLTED) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximal common tree. We show that the MLTED measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. We have implemented our algorithm to compute MLTED exactly and applied it to a variety of data sets successfully. The source code of our method can be found in: https://github.com/khaled-rahman/leafDelTED.

Inference of intra-tumor heterogeneity can provide valuable insight into cancer evolution. Somatic mutations detected by sequencing can help estimate the purity of a tumor sample and reconstruct its subclonal composition. Although several methods have been developed to infer intra-tumor heterogeneity, the majority of these tools rely on variant allele frequencies as estimated via ultra-deep sequencing from multiple samples of the same tumor. In practice, obtaining sequencing data from a large number of samples per patient is only feasible in a few cancer types such as liquid tumors, or in rare cases involving solid tumors selected for research. We introduce CTPsingle, which aims at inferring the subclonal composition by using low-coverage sequencing data from a single tumor sample. We show that CTPsingle is able to infer the purity and the clonality of single-sample tumors with high accuracy, even restricted to a coverage depth of ∼30 × .

Prime numbers are one of the fundamental entities in Number Theory. The guarantee of the existence of a prime number within a certain interval can be helpful in solving several types of problems. The Bertrand-Chebyshev theorem, also known as Bertrand’s postulate, can be very useful in this context. Here we present several solved examples where it can be successfully used. A particular emphasis is placed on Math olympiad-style problems and therefore the article is based solely on elementary techniques. In addition to solved examples, this work also contains a brief historical and theoretical background, a list of some stronger results as well as a set of problems for self-study.

Motivation: CYP2D6 is highly polymorphic gene which encodes the (CYP2D6) enzyme, involved in the metabolism of 20–25% of all clinically prescribed drugs and other xenobiotics in the human body. CYP2D6 genotyping is recommended prior to treatment decisions involving one or more of the numerous drugs sensitive to CYP2D6 allelic composition. In this context, high-throughput sequencing (HTS) technologies provide a promising time-efficient and cost-effective alternative to currently used genotyping techniques. To achieve accurate interpretation of HTS data, however, one needs to overcome several obstacles such as high sequence similarity and genetic recombinations between CYP2D6 and evolutionarily related pseudogenes CYP2D7 and CYP2D8, high copy number variation among individuals and short read lengths generated by HTS technologies. Results: In this work, we present the first algorithm to computationally infer CYP2D6 genotype at basepair resolution from HTS data. Our algorithm is able to resolve complex genotypes, including alleles that are the products of duplication, deletion and fusion events involving CYP2D6 and its evolutionarily related cousin CYP2D7. Through extensive experiments using simulated and real datasets, we show that our algorithm accurately solves this important problem with potential clinical implications. Availability and implementation: Cypiripi is available at http://sfu-compbio.github.io/cypiripi. Contact: cenk@sfu.ca.

MOTIVATION Intra-tumor heterogeneity presents itself through the evolution of subclones during cancer progression. Although recent research suggests that this heterogeneity has clinical implications, in silico determination of the clonal subpopulations remains a challenge. RESULTS We address this problem through a novel combinatorial method, named clonality inference in tumors using phylogeny (CITUP), that infers clonal populations and their frequencies while satisfying phylogenetic constraints and is able to exploit data from multiple samples. Using simulated datasets and deep sequencing data from two cancer studies, we show that CITUP predicts clonal frequencies and the underlying phylogeny with high accuracy. AVAILABILITY AND IMPLEMENTATION CITUP is freely available at: http://sourceforge.net/projects/citup/. CONTACT cenk@sfu.ca SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.