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The chromosomal theory of inheritance dictates that genes on the same chromosome segregate together while genes on different chromosomes assort independently1. Extrachromosomal DNAs (ecDNAs) are common in cancer and drive oncogene amplification, dysregulated gene expression and intratumoural heterogeneity through random segregation during cell division2,3. Distinct ecDNA sequences, termed ecDNA species, can co-exist to facilitate intermolecular cooperation in cancer cells4. How multiple ecDNA species within a tumour cell are assorted and maintained across somatic cell generations is unclear. Here we show that cooperative ecDNA species are coordinately inherited through mitotic co-segregation. Imaging and single-cell analyses show that multiple ecDNAs encoding distinct oncogenes co-occur and are correlated in copy number in human cancer cells. ecDNA species are coordinately segregated asymmetrically during mitosis, resulting in daughter cells with simultaneous copy-number gains in multiple ecDNA species before any selection. Intermolecular proximity and active transcription at the start of mitosis facilitate the coordinated segregation of ecDNA species, and transcription inhibition reduces co-segregation. Computational modelling reveals the quantitative principles of ecDNA co-segregation and co-selection, predicting their observed distributions in cancer cells. Coordinated inheritance of ecDNAs enables co-amplification of specialized ecDNAs containing only enhancer elements and guides therapeutic strategies to jointly deplete cooperating ecDNA oncogenes. Coordinated inheritance of ecDNAs confers stability to oncogene cooperation and novel gene regulatory circuits, allowing winning combinations of epigenetic states to be transmitted across cell generations.

Mismatch repair (MMR)-deficient cancer evolves through the stepwise erosion of coding homopolymers in target genes. Curiously, the MMR genes MutS homolog 6 (MSH6)and MutS homolog 3 (MSH3) also contain coding homopolymers, and these are frequent mutational targets in MMR-deficient cancers. The impact of incremental MMR mutations on MMR-deficient cancer evolution is unknown. Here we show that microsatellite instability modulates DNA repair by toggling hypermutable mononucleotide homopolymer runs in MSH6 and MSH3 through stochastic frameshift switching. Spontaneous mutation and reversion modulate subclonal mutation rate, mutation bias and HLA and neoantigen diversity. Patient-derived organoids corroborate these observations and show that MMR homopolymer sequences drift back into reading frame in the absence of immune selection, suggesting a fitness cost of elevated mutation rates. Combined experimental and simulation studies demonstrate that subclonal immune selection favors incremental MMR mutations. Overall, our data demonstrate that MMR-deficient colorectal cancers fuel intratumor heterogeneity by adapting subclonal mutation rate and diversity to immune selection.

In cancer, evolutionary forces select for clones that evade the immune system. Here we analyzed >10,000 primary tumors and 356 immune-checkpoint-treated metastases using immune dN/dS, the ratio of nonsynonymous to synonymous mutations in the immunopeptidome, to measure immune selection in cohorts and individuals. We classified tumors as immune edited when antigenic mutations were removed by negative selection and immune escaped when antigenicity was covered up by aberrant immune modulation. Only in immune-edited tumors was immune predation linked to CD8 T cell infiltration. Immune-escaped metastases experienced the best response to immunotherapy, whereas immune-edited patients did not benefit, suggesting a preexisting resistance mechanism. Similarly, in a longitudinal cohort, nivolumab treatment removes neoantigens exclusively in the immunopeptidome of nonimmune-edited patients, the group with the best overall survival response. Our work uses dN/dS to differentiate between immune-edited and immune-escaped tumors, measuring potential antigenicity and ultimately helping predict response to treatment.

Genetic and epigenetic variation, together with transcriptional plasticity, contribute to intratumour heterogeneity1. The interplay of these biological processes and their respective contributions to tumour evolution remain unknown. Here we show that intratumour genetic ancestry only infrequently affects gene expression traits and subclonal evolution in colorectal cancer (CRC). Using spatially resolved paired whole-genome and transcriptome sequencing, we find that the majority of intratumour variation in gene expression is not strongly heritable but rather ‘plastic’. Somatic expression quantitative trait loci analysis identified a number of putative genetic controls of expression by cis-acting coding and non-coding mutations, the majority of which were clonal within a tumour, alongside frequent structural alterations. Consistently, computational inference on the spatial patterning of tumour phylogenies finds that a considerable proportion of CRCs did not show evidence of subclonal selection, with only a subset of putative genetic drivers associated with subclone expansions. Spatial intermixing of clones is common, with some tumours growing exponentially and others only at the periphery. Together, our data suggest that most genetic intratumour variation in CRC has no major phenotypic consequence and that transcriptional plasticity is, instead, widespread within a tumour.

Oncogene amplification on extrachromosomal DNA (ecDNA) is a common event, driving aggressive tumor growth, drug resistance and shorter survival. Currently, the impact of nonchromosomal oncogene inheritance—random identity by descent—is poorly understood. Also unclear is the impact of ecDNA on somatic variation and selection. Here integrating theoretical models of random segregation, unbiased image analysis, CRISPR-based ecDNA tagging with live-cell imaging and CRISPR-C, we demonstrate that random ecDNA inheritance results in extensive intratumoral ecDNA copy number heterogeneity and rapid adaptation to metabolic stress and targeted treatment. Observed ecDNAs benefit host cell survival or growth and can change within a single cell cycle. ecDNA inheritance can predict, a priori, some of the aggressive features of ecDNA-containing cancers. These properties are facilitated by the ability of ecDNA to rapidly adapt genomes in a way that is not possible through chromosomal oncogene amplification. These results show how the nonchromosomal random inheritance pattern of ecDNA contributes to poor outcomes for patients with cancer.

Cancers accumulate mutations that lead to neoantigens, novel peptides that elicit an immune response, and consequently undergo evolutionary selection. Here we establish how negative selection shapes the clonality of neoantigens in a growing cancer by constructing a mathematical model of neoantigen evolution. The model predicts that, without immune escape, tumor neoantigens are either clonal or at low frequency; hypermutated tumors can only establish after the evolution of immune escape. Moreover, the site frequency spectrum of somatic variants under negative selection appears more neutral as the strength of negative selection increases, which is consistent with classical neutral theory. These predictions are corroborated by the analysis of neoantigen frequencies and immune escape in exome and RNA sequencing data from 879 colon, stomach and endometrial cancers.

Most cancer genomic data are generated from bulk samples composed of mixtures of cancer subpopulations, as well as normal cells. Subclonal reconstruction methods based on machine learning aim to separate those subpopulations in a sample and infer their evolutionary history. However, current approaches are entirely data driven and agnostic to evolutionary theory. We demonstrate that systematic errors occur in the analysis if evolution is not accounted for, and this is exacerbated with multi-sampling of the same tumor. We present a novel approach for model-based tumor subclonal reconstruction, called MOBSTER, which combines machine learning with theoretical population genetics. Using public whole-genome sequencing data from 2,606 samples from different cohorts, new data and synthetic validation, we show that this method is more robust and accurate than current techniques in single-sample, multiregion and longitudinal data. This approach minimizes the confounding factors of nonevolutionary methods, thus leading to more accurate recovery of the evolutionary history of human cancers.

Mutation accumulation in tumour evolution is one major cause of intra-tumour heterogeneity (ITH), which often leads to drug resistance during treatment. Previous studies with multi-region sequencing have shown that mutation divergence among samples within the patient is common, and the importance of spatial sampling to obtain a complete picture in tumour measurements. However, quantitative comparisons of the relationship between mutation heterogeneity and tumour expansion modes, sampling distances as well as the sampling methods are still few. Here, we investigate how mutations diverge over space by varying the sampling distance and tumour expansion modes using individual-based simulations. We measure ITH by the Jaccard index between samples and quantify how ITH increases with sampling distance, the pattern of which holds in various sampling methods and sizes. We also compare the inferred mutation rates based on the distributions of variant allele frequencies under different tumour expansion modes and sampling sizes. In exponentially fast expanding tumours, a mutation rate can always be inferred for any sampling size. However, the accuracy compared with the true value decreases when the sampling size decreases, where small sampling sizes result in a high estimate of the mutation rate. In addition, such an inference becomes unreliable when the tumour expansion is slow, such as in surface growth.

Subclonal architectures are prevalent across cancer types. However, the temporal evolutionary dynamics that produce tumor subclones remain unknown. Here we measure clone dynamics in human cancers by using computational modeling of subclonal selection and theoretical population genetics applied to high-throughput sequencing data. Our method determined the detectable subclonal architecture of tumor samples and simultaneously measured the selective advantage and time of appearance of each subclone. We demonstrate the accuracy of our approach and the extent to which evolutionary dynamics are recorded in the genome. Application of our method to high-depth sequencing data from breast, gastric, blood, colon and lung cancer samples, as well as metastatic deposits, showed that detectable subclones under selection, when present, consistently emerged early during tumor growth and had a large fitness advantage (>20%). Our quantitative framework provides new insight into the evolutionary trajectories of human cancers and facilitates predictive measurements in individual tumors from widely available sequencing data. This analysis uses computational modeling of clonal selection to measure evolutionary dynamics in primary human cancers. The method employs high-throughput sequencing data and simultaneously measures the selective advantage and time of appearance of subclones.

Cancer, the unregulated proliferation of cells, can occur at any age and may arise from almost all cell types. However, the incidence and types of cancer differ with age. Some cancers are predominantly observed in children, others are mostly restricted to older ages. Treatment strategies of some cancers are very successful and cure is common in childhood, while treatment of the same cancer type is much more challenging in adults. Here, we develop a stochastic model of stem cell proliferation that considers both tissue development and homeostasis and discuss the disturbance of such a system by mutations. Due to changes in population size, mutant fitness becomes context dependent and consequently the effects of mutations on the stem cell population can vary with age. We discuss different mutant phenotypes and show the age dependency of their expected abundances. Most importantly, fitness of particular mutations can change with age and advantageous mutations can become deleterious or vice versa. This perspective can explain unique properties of childhood disorders, for example, the frequently observed phenomenon of a self‐limiting leukemia in newborns with trisomy 21, but also explains other puzzling observations such as the increased risk of leukemia in patients with bone marrow failure or chemotherapy induced myelodysplasia. StemCells2016;34:543–550

Despite extraordinary efforts to profile cancer genomes, interpreting the vast amount of genomic data in the light of cancer evolution remains challenging. Here we demonstrate that neutral tumor evolution results in a power-law distribution of the mutant allele frequencies reported by next-generation sequencing of tumor bulk samples. We find that the neutral power law fits with high precision 323 of 904 cancers from 14 types and from different cohorts. In malignancies identified as evolving neutrally, all clonal selection seemingly occurred before the onset of cancer growth and not in later-arising subclones, resulting in numerous passenger mutations that are responsible for intratumoral heterogeneity. Reanalyzing cancer sequencing data within the neutral framework allowed the measurement, in each patient, of both the in vivo mutation rate and the order and timing of mutations. This result provides a new way to interpret existing cancer genomic data and to discriminate between functional and non-functional intratumoral heterogeneity.

The genomes of cells across human tissues are riddled by changes to their DNA1–3. Many of these mutations do not alter the properties of a cell, and are neutral passengers. However, a small proportion can change a cell’s fitness, and increase or decrease the progeny that originate from the mutated cell4. How many of these alterations under positive selection (drivers) exist in total is unknown. Whether the current list of drivers is almost complete, or whether large proportions of positively selected drivers in the human genome remain undetected is yet to be determined.

Diffuse midline gliomas (DMGs) are highly aggressive, incurable childhood brain tumors. They present a clinical challenge due to many factors, including heterogeneity and diffuse infiltration, complicating disease management. Recent studies have described the existence of subclonal populations that may co-operate to drive pro-tumorigenic processes such as cellular invasion. However, a precise quantification of subclonal interactions is lacking, a problem that extends to other cancers. In this study, we combine spatial computational modeling of cellular interactions during invasion with co-evolution experiments of clonally disassembled patient-derived DMG cells. We design a Bayesian inference framework to quantify spatial subclonal interactions between molecular and phenotypically distinct lineages with different patterns of invasion. We show how this approach could discriminate genuine interactions, where one clone enhanced the invasive phenotype of another, from those apparently only due to the complex dynamics of spatially restricted growth. This study provides a framework for the quantification of subclonal interactions in DMG.

Zahlreiche politökonomische Klassiker unterschiedlichster Schulen waren sich darin einig, dass dem Kapitalismus ein sich gesetzmäßig vollziehender Bedeutungsverlust von Marktprinzipien inhärent sei. Der Beitrag unterzieht auf fünf Feldern wirtschafts- und sozialpolitischer Regulierung Indikatoren der Liberalisierungspolitik für 21 OECD-Länder einer deskriptiven Analyse. Wir zeigen auf, dass die westlichen Industrieländer im starken Gegensatz zu den theoretischen Erwartungen der Klassiker der Politischen Ökonomie einem weitgehend konvergenten Trend marktschaffender Politik unterliegen. Spätestens im Verlauf der ersten Hälfte der 1980er Jahre sind die entwickelten Industrienationen in eine neue Phase wirtschaftlicher Liberalisierung eingetreten, die bis in die Gegenwart anhält. Eine methodische Implikation unserer Befunde legt nahe, dass die Methoden der kausalen Analyse konvergenter Liberalisierungspolitik nicht dieselben sein können wie jene, die zur Analyse der Aufbau- und Konsolidierungsphase der unterschiedlichen Nachkriegskapitalismen zur Anwendung kamen. Political-economic classics of different schools agreed that capitalism inherently and inevitably leads to a decline of market principles. We analyze indicators of liberalization policies for 21 OECD-countries in five economic and social policy fields and demonstrate that western industrialized countries are subject of a convergent trend towards market-creating policies—in stark contrast to the theoretical expectations of several political economy authors. At the latest during the first half of the eighties, the western democracies entered a new phase of economic liberalization, which continues up to the present. A methodological implication of our findings suggests that the methods of causal analysis of convergent liberalization policies may not be the same as those who have been applied for the analysis of development and consolidation of the varieties of capitalism in the postwar era.

AbstractWe define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having a so-called pre-model. As a corollary, we retrieve cut elimination for several axiomatic theories, including Church's simple type theory.

In the version of this article originally published, in the “Theoretical framework of subclonal selection” section of the main text, ref. 11 instead of ref. 19 should have been cited at the end of the phrase “Our previously presented frequentist approach to detect subclonal selection from bulk sequencing data involves an R2test statistic.” The error has been corrected in the HTML and PDF versions of the article.

The cellular age distribution of hierarchically organized tissues can reveal important insights into the dynamics of cell differentiation and self-renewal and associated cancer risks. Here, we examine the effect of progenitor compartments with varying differentiation and self-renewal capacities on the resulting observable distributions of replicative cellular ages. We find that strongly amplifying progenitor compartments, i.e. compartments with high self-renewal capacities, substantially broaden the age distributions which become skewed towards younger cells with a long tail of few old cells. For several of these strongly amplifying compartments, the age distribution becomes virtually independent of the influx from the stem cell compartment. By contrast, if tissues are organized into many downstream compartments with low self-renewal capacity, the shape of the replicative cell distribution in more differentiated compartments is dominated by stem cell dynamics with little added variation. In the limiting case of a strict binary differentiation tree without self-renewal, the shape of the output distribution becomes indistinguishable from that of the input distribution. Our results suggest that a comparison of cellular age distributions between healthy and cancerous tissues may inform about dynamical changes within the hierarchical tissue structure, i.e. an acquired increased self-renewal capacity in certain tumours. Furthermore, we compare our theoretical results to telomere length distributions in granulocyte populations of 10 healthy individuals across different ages, highlighting that our theoretical expectations agree with experimental observations.

No relevant conflicts of interest to declare.

Introduction:Acquired aplastic anemia (AA) is typically characterized by pancytopenia and bone marrow (BM) failure mostly due to an autoimmune attack against the hematopoietic stem cell compartment. Thus, AA patients frequently respond to immunosuppressive therapy (IST). Hypoplastic myelodysplastic syndrome (hMDS) frequently mimics clinical and morphological features of AA and proper clinical discrimination of hMDS from AA sometimes remains difficult. Interestingly, some cases of hMDS respond at least partially to IST and on the other hand, AA can clonally evolve to hMDS. Telomeres shorten with each cell division and telomere length (TL) reflects the replicative potential of somatic cells. Whereas it is proposed that TL can to some degree discriminate hereditary subtypes of bone marrow failure syndromes from classical acquired forms, the role of TL for disease pathogenesis in hMDS remains unclear. In this study, we therefore aimed to investigate accelerated TL shortening as a possible (bio-)marker to distinguish hMDS from AA.

Cancers are rarely caused by single mutations, but often develop as a result of the combined effects of multiple mutations. For most cells, the number of possible cell divisions is limited because of various biological constraints, such as progressive telomere shortening, cell senescence cascades or a hierarchically organized tissue structure. Thus, the risk of accumulating cells carrying multiple mutations is low. Nonetheless, many diseases are based on the accumulation of such multiple mutations. We model a general, hierarchically organized tissue by a multi-compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters. We show that hierarchically organized tissues strongly suppress cells carrying multiple mutations and derive closed solutions for the expected size and diversity of clonal populations founded by a single mutant within the hierarchy. We discuss the example of childhood acute lymphoblastic leukaemia in detail and find good agreement between our predicted results and recently observed clonal diversities in patients. This result can contribute to the explanation of very diverse mutation profiles observed by whole genome sequencing of many different cancers.