Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

A polygenic burden of rare disruptive mutations in schizophrenia.

Schizophrenia is a common disease with a complex aetiology, probably involving multiple and heterogeneous genetic factors. Here, by analysing the exome sequences of 2,536 schizophrenia cases and 2,543 controls, we demonstrate a polygenic burden primarily arising from rare (less than 1 in 10,000), disruptive mutations distributed across many genes. Particularly enriched gene sets include the voltage-gated calcium ion channel and the signalling complex formed by the activity-regulated cytoskeleton-associated scaffold protein (ARC) of the postsynaptic density, sets previously implicated by genome-wide association and copy-number variation studies. Similar to reports in autism, targets of the fragile X mental retardation protein (FMRP, product of FMR1) are enriched for case mutations. No individual gene-based test achieves significance after correction for multiple testing and we do not detect any alleles of moderately low frequency (approximately 0.5 to 1 per cent) and moderately large effect. Taken together, these data suggest that population-based exome sequencing can discover risk alleles and complements established gene-mapping paradigms in neuropsychiatric disease

Interpreting the role of de novo protein-coding mutations in neuropsychiatric disease

Pedigree, linkage and association studies are consistent with heritable variation for complex disease due to the segregation of genetic factors in families and in the population. In contrast, de novo mutations make only minor contributions to heritability estimates for complex traits. Nonetheless, some de novo variants are known to be important in disease etiology. The identification of risk-conferring de novo variants will contribute to the discovery of etiologically relevant genes and pathways and may help in genetic counseling. There is considerable interest in the role of such mutations in complex neuropsychiatric disease, largely driven by new genotyping and sequencing technologies. An important role for large de novo copy number variations has been established. Recently, whole-exome sequencing has been used to extend the investigation of de novo variation to point mutations in protein-coding regions. Here, we consider several challenges for the interpretation of such mutations in the context of their role in neuropsychiatric disease

Whole-exome sequencing and clinical interpretation of FFPE tumor samples to guide precision cancer medicine

Translating whole exome sequencing (WES) for prospective clinical use may impact the care of cancer patients; however, multiple innovations are necessary for clinical implementation. These include: (1) rapid and robust WES from formalin-fixed paraffin embedded (FFPE) tumor tissue, (2) analytical output similar to data from frozen samples, and (3) clinical interpretation of WES data for prospective use. Here, we describe a prospective clinical WES platform for archival FFPE tumor samples. The platform employs computational methods for effective clinical analysis and interpretation of WES data. When applied retrospectively to 511 exomes, the interpretative framework revealed a “long tail” of somatic alterations in clinically important genes. Prospective application of this approach identified clinically relevant alterations in 15/16 patients. In one patient, previously undetected findings guided clinical trial enrollment leading to an objective clinical response. Overall, this methodology may inform the widespread implementation of precision cancer medicine

Exome sequencing of pleuropulmonary blastoma reveals frequent biallelic loss of TP53 and two hits in DICER1 resulting in retention of 5p-derived miRNA hairpin loop sequences

Pleuropulmonary blastoma is a rare childhood malignancy of lung mesenchymal cells that can remain dormant as epithelial cysts or progress to high-grade sarcoma. Predisposing germline loss-of-function DICER1 variants have been described. We sought to uncover additional contributors through whole exome sequencing of 15 tumor/normal pairs, followed by targeted resequencing, miRNA analysis and immunohistochemical analysis of additional tumors. In addition to frequent biallelic loss of TP53 and mutations of NRAS or BRAF in some cases, each case had compound disruption of DICER1: a germline (12 cases) or somatic (3 cases) loss-of-function variant plus a somatic missense mutation in the RNase IIIb domain. 5p-Derived microRNA (miRNA) transcripts retained abnormal precursor miRNA loop sequences normally removed by DICER1. This work both defines a genetic interaction landscape with DICER1 mutation and provides evidence for alteration in miRNA transcripts as a consequence of DICER1 disruption in cancer

Meta-Analysis of Gene Level Tests for Rare Variant Association

The vast majority of connections between complex disease and common genetic variants were identified through meta-analysis, a powerful approach that enables large sample sizes while protecting against common artifacts due to population structure, repeated small sample analyses, and/or limitations with sharing individual level data. As the focus of genetic association studies shifts to rare variants, genes and other functional units are becoming the unit of analysis. Here, we propose and evaluate new approaches for performing meta-analysis of rare variant association tests, including burden tests, weighted burden tests, variable threshold tests and tests that allow variants with opposite effects to be grouped together. We show that our approach retains useful features of single variant meta-analytic approaches and demonstrate its utility in a study of blood lipid levels in ∼18,500 individuals genotyped with exome arrays

Mutational heterogeneity in cancer and the search for new cancer genes

Major international projects are now underway aimed at creating a comprehensive catalog of all genes responsible for the initiation and progression of cancer. These studies involve sequencing of matched tumor–normal samples followed by mathematical analysis to identify those genes in which mutations occur more frequently than expected by random chance. Here, we describe a fundamental problem with cancer genome studies: as the sample size increases, the list of putatively significant genes produced by current analytical methods burgeons into the hundreds. The list includes many implausible genes (such as those encoding olfactory receptors and the muscle protein titin), suggesting extensive false positive findings that overshadow true driver events. Here, we show that this problem stems largely from mutational heterogeneity and provide a novel analytical methodology, MutSigCV, for resolving the problem. We apply MutSigCV to exome sequences from 3,083 tumor-normal pairs and discover extraordinary variation in (i) mutation frequency and spectrum within cancer types, which shed light on mutational processes and disease etiology, and (ii) mutation frequency across the genome, which is strongly correlated with DNA replication timing and also with transcriptional activity. By incorporating mutational heterogeneity into the analyses, MutSigCV is able to eliminate most of the apparent artefactual findings and allow true cancer genes to rise to attention

The genetic landscape of high-risk neuroblastoma

Neuroblastoma is a malignancy of the developing sympathetic nervous system that often presents with widespread metastatic disease, resulting in survival rates of less than 50%1. To determine the spectrum of somatic mutation in high-risk neuroblastoma, we studied 240 cases using a combination of whole exome, genome and transcriptome sequencing as part of the Therapeutically Applicable Research to Generate Effective Treatments (TARGET) initiative. Here we report a low median exonic mutation frequency of 0.60 per megabase (0.48 non-silent), and remarkably few recurrently mutated genes in these tumors. Genes with significant somatic mutation frequencies included ALK (9.2% of cases), PTPN11 (2.9%), ATRX (2.5%, an additional 7.1% had focal deletions), MYCN (1.7%, a recurrent p.Pro44Leu alteration), and NRAS (0.83%). Rare, potentially pathogenic germline variants were significantly enriched in ALK, CHEK2, PINK1, and BARD1. The relative paucity of recurrent somatic mutations in neuroblastoma challenges current therapeutic strategies reliant upon frequently altered oncogenic drivers

Comprehensive analysis of cancer-associated somatic mutations in class I HLA genes

Detection of somatic mutations in human leukocyte antigen (HLA) genes using whole-exome sequencing (WES) is hampered by the high polymorphism of the HLA loci, which prevents alignment of sequencing reads to the human reference genome. We describe a computational pipeline that enables accurate inference of germline alleles of class I HLA-A, B and C genes and subsequent detection of mutations in these genes using the inferred alleles as a reference. Analysis of WES data from 7,930 pairs of tumor and healthy tissue from the same patient revealed 298 nonsilent HLA mutations in tumors from 266 patients. These 298 mutations are enriched for likely functional mutations, including putative loss-of-function events. Recurrence of mutations suggested that these \u27hotspot\u27 sites were positively selected. Cancers with recurrent somatic HLA mutations were associated with upregulation of signatures of cytolytic activity characteristic of tumor infiltration by effector lymphocytes, supporting immune evasion by altered HLA function as a contributory mechanism in cancer