The complexity of genome rearrangement combinatorics under the infinite sites model.

Rearrangements are discrete processes whereby discrete segments of DNA are deleted, replicated and inserted into novel positions. A sequence of such configurations, termed a rearrangement evolution, results in jumbled DNA arrangements, frequently observed in cancer genomes. We introduce a method that allows us to precisely count these different evolutions for a range of processes including breakage-fusion-bridge-cycles, tandem-duplications, inverted-duplications, reversals, transpositions and deletions, showing that the space of rearrangement evolution is super-exponential in size. These counts assume the infinite sites model of unique breakpoint usage.

PDE MODELS OF ADDER MECHANISMS IN CELLULAR PROLIFERATION.

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.

Heterarchy of transcription factors driving basal and luminal cell phenotypes in human urothelium.

Cell differentiation is affected by complex networks of transcription factors that co-ordinate re-organisation of the chromatin landscape. The hierarchies of these relationships can be difficult to dissect. During in vitro differentiation of normal human uro-epithelial cells, formaldehyde-assisted isolation of regulatory elements (FAIRE-seq) and RNA-seq was used to identify alterations in chromatin accessibility and gene expression changes following activation of the nuclear receptor peroxisome proliferator-activated receptor gamma (PPARγ) as a differentiation-initiating event. Regions of chromatin identified by FAIRE-seq, as having altered accessibility during differentiation, were found to be enriched with sequence-specific binding motifs for transcription factors predicted to be involved in driving basal and differentiated urothelial cell phenotypes, including forkhead box A1 (FOXA1), P63, GRHL2, CTCF and GATA-binding protein 3 (GATA3). In addition, co-occurrence of GATA3 motifs was observed within subsets of differentiation-specific peaks containing P63 or FOXA1. Changes in abundance of GRHL2, GATA3 and P63 were observed in immunoblots of chromatin-enriched extracts. Transient siRNA knockdown of P63 revealed that P63 favoured a basal-like phenotype by inhibiting differentiation and promoting expression of basal marker genes. GATA3 siRNA prevented differentiation-associated downregulation of P63 protein and transcript, and demonstrated positive feedback of GATA3 on PPARG transcript, but showed no effect on FOXA1 transcript or protein expression. This approach indicates that as a transcriptionally regulated programme, urothelial differentiation operates as a heterarchy, wherein GATA3 is able to co-operate with FOXA1 to drive expression of luminal marker genes, but that P63 has potential to transrepress expression of the same genes.

A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations.

We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies.

Kinetic theory of age-structured stochastic birth-death processes.

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Inferring the Clonal Structure of Viral Populations from Time Series Sequencing.

RNA virus populations will undergo processes of mutation and selection resulting in a mixed population of viral particles. High throughput sequencing of a viral population subsequently contains a mixed signal of the underlying clones. We would like to identify the underlying evolutionary structures. We utilize two sources of information to attempt this; within segment linkage information, and mutation prevalence. We demonstrate that clone haplotypes, their prevalence, and maximum parsimony reticulate evolutionary structures can be identified, although the solutions may not be unique, even for complete sets of information. This is applied to a chain of influenza infection, where we infer evolutionary structures, including reassortment, and demonstrate some of the difficulties of interpretation that arise from deep sequencing due to artifacts such as template switching during PCR amplification.

Cardio-oncology: an ongoing evolution.

Cancer survivorship has been greatly impacted with the development of modern cancer treatments. While significant strides have been made in managing many types of cancer, now physicians face new challenges. Over the past decades, cardiovascular events in cancer survivors have increased in prevalence, driving the development of multidisciplinary cardio-oncology programs. Additionally, as cancer patients live longer, their risk of developing secondary cardiovascular events increases. The rapid development of novel cancer therapies will continue to generate questions of cardiac risk and cardiac protection in cancer patients over time. We wish to outline the development of cardio-oncology in its present state, and provide future perspectives for the discipline.

Exon Skipping Is Correlated with Exon Circularization.

Circular RNAs are found in a wide range of organisms and it has been proposed that they perform disparate functions. However, how RNA circularization is connected to alternative splicing remains largely unexplored. Here, we stimulated primary human endothelial cells with tumor necrosis factor α or tumor growth factor ß, purified RNA, generated >2.4 billion RNA-seq reads, and used a custom pipeline to characterize circular RNAs derived from coding exons. We find that circularization of exons is widespread and correlates with exon skipping, a feature that adds considerably to the regulatory complexity of the human transcriptome.

The relative timing of mutations in a breast cancer genome.

Many tumors have highly rearranged genomes, but a major unknown is the relative importance and timing of genome rearrangements compared to sequence-level mutation. Chromosome instability might arise early, be a late event contributing little to cancer development, or happen as a single catastrophic event. Another unknown is which of the point mutations and rearrangements are selected. To address these questions we show, using the breast cancer cell line HCC1187 as a model, that we can reconstruct the likely history of a breast cancer genome. We assembled probably the most complete map to date of a cancer genome, by combining molecular cytogenetic analysis with sequence data. In particular, we assigned most sequence-level mutations to individual chromosomes by sequencing of flow sorted chromosomes. The parent of origin of each chromosome was assigned from SNP arrays. We were then able to classify most of the mutations as earlier or later according to whether they occurred before or after a landmark event in the evolution of the genome, endoreduplication (duplication of its entire genome). Genome rearrangements and sequence-level mutations were fairly evenly divided earlier and later, suggesting that genetic instability was relatively constant throughout the life of this tumor, and chromosome instability was not a late event. Mutations that caused chromosome instability would be in the earlier set. Strikingly, the great majority of inactivating mutations and in-frame gene fusions happened earlier. The non-random timing of some of the mutations may be evidence that they were selected.

The landscape of cancer genes and mutational processes in breast cancer.

All cancers carry somatic mutations in their genomes. A subset, known as driver mutations, confer clonal selective advantage on cancer cells and are causally implicated in oncogenesis, and the remainder are passenger mutations. The driver mutations and mutational processes operative in breast cancer have not yet been comprehensively explored. Here we examine the genomes of 100 tumours for somatic copy number changes and mutations in the coding exons of protein-coding genes. The number of somatic mutations varied markedly between individual tumours. We found strong correlations between mutation number, age at which cancer was diagnosed and cancer histological grade, and observed multiple mutational signatures, including one present in about ten per cent of tumours characterized by numerous mutations of cytosine at TpC dinucleotides. Driver mutations were identified in several new cancer genes including AKT2, ARID1B, CASP8, CDKN1B, MAP3K1, MAP3K13, NCOR1, SMARCD1 and TBX3. Among the 100 tumours, we found driver mutations in at least 40 cancer genes and 73 different combinations of mutated cancer genes. The results highlight the substantial genetic diversity underlying this common disease.

Tandem duplication of chromosomal segments is common in ovarian and breast cancer genomes.

The application of paired-end next generation sequencing approaches has made it possible to systematically characterize rearrangements of the cancer genome to base-pair level. Utilizing this approach, we report the first detailed analysis of ovarian cancer rearrangements, comparing high-grade serous and clear cell cancers, and these histotypes with other solid cancers. Somatic rearrangements were systematically characterized in eight high-grade serous and five clear cell ovarian cancer genomes and we report here the identification of > 600 somatic rearrangements. Recurrent rearrangements of the transcriptional regulator gene, TSHZ3, were found in three of eight serous cases. Comparison to breast, pancreatic and prostate cancer genomes revealed that a subset of ovarian cancers share a marked tandem duplication phenotype with triple-negative breast cancers. The tandem duplication phenotype was not linked to BRCA1/2 mutation, suggesting that other common mechanisms or carcinogenic exposures are operative. High-grade serous cancers arising in women with germline BRCA1 or BRCA2 mutation showed a high frequency of small chromosomal deletions. These findings indicate that BRCA1/2 germline mutation may contribute to widespread structural change and that other undefined mechanism(s), which are potentially shared with triple-negative breast cancer, promote tandem chromosomal duplications that sculpt the ovarian cancer genome.

Systematic identification of genomic markers of drug sensitivity in cancer cells.

Clinical responses to anticancer therapies are often restricted to a subset of patients. In some cases, mutated cancer genes are potent biomarkers for responses to targeted agents. Here, to uncover new biomarkers of sensitivity and resistance to cancer therapeutics, we screened a panel of several hundred cancer cell lines--which represent much of the tissue-type and genetic diversity of human cancers--with 130 drugs under clinical and preclinical investigation. In aggregate, we found that mutated cancer genes were associated with cellular response to most currently available cancer drugs. Classic oncogene addiction paradigms were modified by additional tissue-specific or expression biomarkers, and some frequently mutated genes were associated with sensitivity to a broad range of therapeutic agents. Unexpected relationships were revealed, including the marked sensitivity of Ewing's sarcoma cells harbouring the EWS (also known as EWSR1)-FLI1 gene translocation to poly(ADP-ribose) polymerase (PARP) inhibitors. By linking drug activity to the functional complexity of cancer genomes, systematic pharmacogenomic profiling in cancer cell lines provides a powerful biomarker discovery platform to guide rational cancer therapeutic strategies.

Estimation of rearrangement phylogeny for cancer genomes.

Cancer genomes are complex, carrying thousands of somatic mutations including base substitutions, insertions and deletions, rearrangements, and copy number changes that have been acquired over decades. Recently, technologies have been introduced that allow generation of high-resolution, comprehensive catalogs of somatic alterations in cancer genomes. However, analyses of these data sets generally do not indicate the order in which mutations have occurred, or the resulting karyotype. Here, we introduce a mathematical framework that begins to address this problem. By using samples with accurate data sets, we can reconstruct relatively complex temporal sequences of rearrangements and provide an assembly of genomic segments into digital karyotypes. For cancer genes mutated in rearranged regions, this information can provide a chronological examination of the selective events that have taken place.

Model-integrated estimation of normal tissue contamination for cancer SNP allelic copy number data.

SNP allelic copy number data provides intensity measurements for the two different alleles separately. We present a method that estimates the number of copies of each allele at each SNP position, using a continuous-index hidden Markov model. The method is especially suited for cancer data, since it includes the fraction of normal tissue contamination, often present when studying data from cancer tumors, into the model. The continuous-index structure takes into account the distances between the SNPs, and is thereby appropriate also when SNPs are unequally spaced. In a simulation study we show that the method performs favorably compared to previous methods even with as much as 70% normal contamination. We also provide results from applications to clinical data produced using the Affymetrix genome-wide SNP 6.0 platform.

Germline fitness-based scoring of cancer mutations.

A key goal in cancer research is to find the genomic alterations that underlie malignant cells. Genomics has proved successful in identifying somatic variants at a large scale. However, it has become evident that a typical cancer exhibits a heterogenous mutation pattern across samples. Cases where the same alteration is observed repeatedly seem to be the exception rather than the norm. Thus, pinpointing the key alterations (driver mutations) from a background of variations with no direct causal link to cancer (passenger mutations) is difficult. Here we analyze somatic missense mutations from cancer samples and their healthy tissue counterparts (germline mutations) from the viewpoint of germline fitness. We calibrate a scoring system from protein domain alignments to score mutations and their target loci. We show first that this score predicts to a good degree the rate of polymorphism of the observed germline variation. The scoring is then applied to somatic mutations. We show that candidate cancer genes prone to copy number loss harbor mutations with germline fitness effects that are significantly more deleterious than expected by chance. This suggests that missense mutations play a driving role in tumor suppressor genes. Furthermore, these mutations fall preferably onto loci in sequence neighborhoods that are high scoring in terms of germline fitness. In contrast, for somatic mutations in candidate onco genes we do not observe a statistically significant effect. These results help to inform how to exploit germline fitness predictions in discovering new genes and mutations responsible for cancer.

Exome sequencing identifies frequent mutation of the SWI/SNF complex gene PBRM1 in renal carcinoma.

The genetics of renal cancer is dominated by inactivation of the VHL tumour suppressor gene in clear cell carcinoma (ccRCC), the commonest histological subtype. A recent large-scale screen of ∼3,500 genes by PCR-based exon re-sequencing identified several new cancer genes in ccRCC including UTX (also known as KDM6A), JARID1C (also known as KDM5C) and SETD2 (ref. 2). These genes encode enzymes that demethylate (UTX, JARID1C) or methylate (SETD2) key lysine residues of histone H3. Modification of the methylation state of these lysine residues of histone H3 regulates chromatin structure and is implicated in transcriptional control. However, together these mutations are present in fewer than 15% of ccRCC, suggesting the existence of additional, currently unidentified cancer genes. Here, we have sequenced the protein coding exome in a series of primary ccRCC and report the identification of the SWI/SNF chromatin remodelling complex gene PBRM1 (ref. 4) as a second major ccRCC cancer gene, with truncating mutations in 41% (92/227) of cases. These data further elucidate the somatic genetic architecture of ccRCC and emphasize the marked contribution of aberrant chromatin biology.

Massive genomic rearrangement acquired in a single catastrophic event during cancer development.

Cancer is driven by somatically acquired point mutations and chromosomal rearrangements, conventionally thought to accumulate gradually over time. Using next-generation sequencing, we characterize a phenomenon, which we term chromothripsis, whereby tens to hundreds of genomic rearrangements occur in a one-off cellular crisis. Rearrangements involving one or a few chromosomes crisscross back and forth across involved regions, generating frequent oscillations between two copy number states. These genomic hallmarks are highly improbable if rearrangements accumulate over time and instead imply that nearly all occur during a single cellular catastrophe. The stamp of chromothripsis can be seen in at least 2%-3% of all cancers, across many subtypes, and is present in ∼25% of bone cancers. We find that one, or indeed more than one, cancer-causing lesion can emerge out of the genomic crisis. This phenomenon has important implications for the origins of genomic remodeling and temporal emergence of cancer.

GLO1-A novel amplified gene in human cancer.

To identify a novel amplified cancer gene a systematic screen of 975 human cancer DNA samples, 750 cell lines and 225 primary tumors, using the Affymetrix 10K SNP microarray was undertaken. The screen identified 193 amplicons. A previously uncharacterized amplicon located on 6p21.2 whose 1 Mb minimal common amplified region contained eight genes (GLO1, DNAH8, GLP1R, C6orf64, KCNK5, KCNK17, KCNK16, and C6orf102) was further investigated to determine which gene(s) are the biological targets of this amplicon. Real time quantitative PCR (qPCR) analysis of all amplicon 6p21.2 genes in 618 human cancer cell lines identified GLO1, encoding glyoxalase 1, to be the most frequently amplified gene [twofold or greater amplification in 8.4% (49/536) of cancers]. Also the association between amplification and overexpression was greatest for GLO1. RNAi knockdown of GLO1 had the greatest and most consistent impact on cell accumulation and apoptosis. Cell lines with GLO1 amplification were more sensitive to inhibition of GLO1 by bromobenzylglutathione cyclopentyl diester (BBGC). Subsequent qPCR of 520 primary tumor samples identified twofold and greater amplification of GLO1 in 8/37 (22%) of breast, 12/71 (17%) of sarcomas, 6/53 (11.3%) of nonsmall cell lung, 2/23 (8.7%) of bladder, 6/93 (6.5%) of renal and 5/83 (6%) of gastric cancers. Amplification of GLO1 was rare in colon cancer (1/35) and glioma (1/94). Collectively the results indicate that GLO1 is at least one of the targets of gene amplification on 6p21.2 and may represent a useful target for therapy in cancers with GLO1 amplification.