Search

Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . Let $\Lambda $ be an R-order such that $Q\Lambda $ is a separable Q-algebra. Maranda showed that there exists $k\in \mathbb {N}$ such that for all $\Lambda $ -lattices L and M, if $L/L\pi ^k\simeq M/M\pi ^k$ , then $L\simeq M$ . Moreover, if R is complete and L is an indecomposable $\Lambda $ -lattice, then $L/L\pi ^k$ is also indecomposable. We extend Maranda’s theorem to the class of R-reduced R-torsion-free pure-injective $\Lambda $ -modules.As an application of this extension, we show that if $\Lambda $ is an order over a Dedekind domain R with field of fractions Q such that $Q\Lambda $ is separable, then the lattice of open subsets of the R-torsion-free part of the right Ziegler spectrum of $\Lambda $ is isomorphic to the lattice of open subsets of the R-torsion-free part of the left Ziegler spectrum of $\Lambda $ .Furthermore, with k as in Maranda’s theorem, we show that if M is R-torsion-free and $H(M)$ is the pure-injective hull of M, then $H(M)/H(M)\pi ^k$ is the pure-injective hull of $M/M\pi ^k$ . We use this result to give a characterization of R-torsion-free pure-injective $\Lambda $ -modules and describe the pure-injective hulls of certain R-torsion-free $\Lambda $ -modules.

In this article, we give elementary conditions completely characterising when the theory of modules of a Prüfer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is decidable.

In this paper we prove that the Ziegler spectra of all serial rings are sober. We then use this proof to give a general framework for computing and understanding Ziegler spectra of uniserial rings up to topological indistinguishability. Finally, we illustrate this technique by computing the Ziegler spectra of all rank one uniserial domains up to topological indistinguishability., Comment: 30 pages

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For Bézout domains these conditions are also necessary.

We study the R-torsionfree part of the Ziegler spectrum of an order \Lambda over a Dedekind domain R. We underline and comment on the role of lattices over \Lambda. We describe the torsionfree part of the spectrum when \Lambda is of finite lattice representation type.

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prufer (in particular Bezout) domains whose localizations at maximal ideals have dense value groups. For Bezout domains, these conditions are also necessary.

Extending work of Puninski, Puninskaya and Toffalori in [5], we show that if V is an effectively given valuation domain then the theory of all V-modules is decidable if and only if there exists an algorithm which, given a, b ε V, answers whether a ε rad(bV). This was conjectured in [5] for valuation domains with dense value group, where it was proved for valuation domains with dense archimedean value group. The only ingredient missing from [5] to extend the result to valuation domains with dense value group or infinite residue field is an algorithm which decides inclusion for finite unions of Ziegler open sets. We go on to give an example of a valuation domain with infinite Krull dimension, which has decidable theory of modules with respect to one effective presentation and undecidable theory of modules with respect to another. We show that for this to occur infinite Krull dimension is necessary.

CONTEXT: The tumorigenic role of genetic abnormalities in sporadic pituitary nonfunctioning adenomas (NFAs), which usually originate from gonadotroph cells, is unknown. OBJECTIVE: The objective of the study was to identify somatic genetic abnormalities in sporadic pituitary NFAs. DESIGN: Whole-exome sequencing was performed using DNA from 7 pituitary NFAs and leukocyte samples obtained from the same patients. Somatic variants were confirmed by dideoxynucleotide sequencing, and candidate driver genes were assessed in an additional 24 pituitary NFAs. RESULTS: Whole-exome sequencing achieved a high degree of coverage such that approximately 97% of targeted bases were represented by more than 10 base reads; 24 somatic variants were identified and confirmed in the discovery set of 7 pituitary NFAs (mean 3.5 variants/tumor; range 1-7). Approximately 80% of variants occurred as missense single nucleotide variants and the remainder were synonymous changes or small frameshift deletions. Each of the 24 mutations occurred in independent genes with no recurrent mutations. Mutations were not observed in genes previously associated with pituitary tumorigenesis, although somatic variants in putative driver genes including platelet-derived growth factor D (PDGFD), N-myc down-regulated gene family member 4 (NDRG4), and Zipper sterile-α-motif kinase (ZAK) were identified; however, DNA sequence analysis of these in the validation set of 24 pituitary NFAs did not reveal any mutations indicating that these genes are unlikely to contribute significantly in the etiology of sporadic pituitary NFAs. CONCLUSIONS: Pituitary NFAs harbor few somatic mutations consistent with their low proliferation rates and benign nature, but mechanisms other than somatic mutation are likely involved in the etiology of sporadic pituitary NFAs.

Many neurological conditions are caused by immensely heterogeneous gene mutations. The diagnostic process is often long and complex with most patients undergoing multiple invasive and costly investigations without ever reaching a conclusive molecular diagnosis. The advent of massively parallel, next-generation sequencing promises to revolutionize genetic testing and shorten the ‘diagnostic odyssey’ for many of these patients. We performed a pilot study using heterogeneous ataxias as a model neurogenetic disorder to assess the introduction of next-generation sequencing into clinical practice. We captured 58 known human ataxia genes followed by Illumina Next-Generation Sequencing in 50 highly heterogeneous patients with ataxia who had been extensively investigated and were refractory to diagnosis. All cases had been tested for spinocerebellar ataxia 1–3, 6, 7 and Friedrich’s ataxia and had multiple other biochemical, genetic and invasive tests. In those cases where we identified the genetic mutation, we determined the time to diagnosis. Pathogenicity was assessed using a bioinformatics pipeline and novel variants were validated using functional experiments. The overall detection rate in our heterogeneous cohort was 18% and varied from 8.3% in those with an adult onset progressive disorder to 40% in those with a childhood or adolescent onset progressive disorder. The highest detection rate was in those with an adolescent onset and a family history (75%). The majority of cases with detectable mutations had a childhood onset but most are now adults, reflecting the long delay in diagnosis. The delays were primarily related to lack of easily available clinical testing, but other factors included the presence of atypical phenotypes and the use of indirect testing. In the cases where we made an eventual diagnosis, the delay was 3–35 years (mean 18.1 years). Alignment and coverage metrics indicated that the capture and sequencing was highly efficient and the consumable cost was ∼£400 (€460 or US$620). Our pathogenicity interpretation pathway predicted 13 different mutations in eight different genes: PRKCG, TTBK2, SETX, SPTBN2, SACS, MRE11, KCNC3 and DARS2 of which nine were novel including one causing a newly described recessive ataxia syndrome. Genetic testing using targeted capture followed by next-generation sequencing was efficient, cost-effective, and enabled a molecular diagnosis in many refractory cases. A specific challenge of next-generation sequencing data is pathogenicity interpretation, but functional analysis confirmed the pathogenicity of novel variants showing that the pipeline was robust. Our results have broad implications for clinical neurology practice and the approach to diagnostic testing.

Adaptor protein-2 (AP2), a central component of clathrin-coated vesicles (CCVs), is pivotal in clathrin-mediated endocytosis which internalises plasma membrane constituents such as G protein-coupled receptors (GPCRs)1-3 . AP2, a heterotetramer of alpha, beta, mu and sigma subunits, links clathrin to vesicle membranes and binds to tyrosine-based and dileucine-based motifs of membrane-associated cargo proteins1,4. Here, we show that AP2 sigma subunit (AP2S1) missense mutations, which all involved the Arg15 residue (Arg15Cys, Arg15His and Arg15Leu) that forms key contacts with dileucine-based motifs of CCV cargo proteins4, result in familial hypocalciuric hypercalcemia type 3 (FHH3), an extracellular-calcium homeostasis disorder affecting parathyroids, kidneys and bone5-7 These AP2S1 mutations occurred in >20% of FHH patients without calcium-sensing GPCR (CaSR) mutations which cause FHH18-12. AP2S1 mutations decreased the sensitivity of CaSR-expressing cells to extracellular-calcium and reduced CaSR endocytosis, likely through a loss of interaction with a C-terminus CaSR dileucine-based motif whose disruption also decreased intracellular signalling. Thus, our results reveal a new role for AP2 in extracellular-calcium homeostasis.

We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra (over a recursively given field) is tame if and only its common theory of modules is decidable. Moreover, as a corollary, we are able to confirm this conjecture for the class of concealed canonical algebras over algebraically closed fields. These are the first examples of non-domestic algebras which have been shown to have decidable theory of modules., The results have been extended to cover all tubular algebras rather than just canonical algebras of tubular type - the title and abstract have been changed to reflect this. Moreover, the counter example to corollary 8.8 of Prest and Harland's paper "Modules with irrational slope over tubular algebras" has be replaced by a proof that that corollary does not hold for any tubular algebra. 47 pages

We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of modules of finite-dimensional algebras induce embeddings of lattices of pp formulas and hence are non-decreasing on Krull-Gabriel dimension and uniserial dimension. A consequence is that the category of modules of any wild finite-dimensional algebra has width $\infty$ and hence, if the algebra is countable, there is a superdecomposable pure-injective representation. It is conjectured that a stronger result is true: that a representation embedding from ${\rm Mod}\mbox{-}S$ to ${\rm Mod}\mbox{-}R$ admits an inverse interpretation functor from its image and hence that, in this case, ${\rm Mod}\mbox{-}R$ interprets ${\rm Mod}\mbox{-}S$. This would imply, for instance, that every wild category of modules interprets the (undecidable) word problem for (semi)groups. We show that the conjecture holds for finitely controlled representation embeddings. Finally we prove that if $R,S$ are finite dimensional algebras over an algebraically closed field and $I:{\rm Mod}\mbox{-}R\rightarrow{\rm Mod}\mbox{-}S$ is an interpretation functor such that the smallest definable subcategory containing the image of $I$ is the whole of ${\rm Mod}\mbox{-}S$ then, if $R$ is tame, so is $S$ and similarly, if $R$ is domestic, then $S$ also is domestic., Comment: More results added

CONTEXT: Genetic abnormalities, such as those of multiple endocrine neoplasia type 1 (MEN1) and Cyclin D1 (CCND1) genes, occur in

New sequencing technologies can address diverse biomedical questions but are limited by a minimum required DNA input of typically 1 μg. We describe how sequencing libraries can be reproducibly created from 20 pg of input DNA using a modified transpososome-mediated fragmentation technique. Resulting libraries incorporate in-line bar-coding, which facilitates sample multiplexes that can be sequenced using Illumina platforms with the manufacturer's sequencing primer. We demonstrate this technique by providing deep coverage sequence of the Escherichia coli K-12 genome that shows equivalent target coverage to a 1-μg input library prepared using standard Illumina methods. Reducing template quantity does, however, increase the proportion of duplicate reads and enriches coverage in low-GC regions. This finding was confirmed with exhaustive resequencing of a mouse library constructed from 20 pg of gDNA input (about seven haploid genomes) resulting in ∼0.4-fold statistical coverage of uniquely mapped fragments. This implies that a near-complete coverage of the mouse genome is obtainable with this approach using 20 genomes as input. Application of this new method now allows genomic studies from low mass samples and routine preparation of sequencing libraries from enrichment procedures.

SummaryEnhancers determine tissue-specific gene expression programs. Enhancers are marked by high histone H3 lysine 4 mono-methylation (H3K4me1) and by the acetyl-transferase p300, which has allowed genome-wide enhancer identification. However, the regulatory principles by which subsets of enhancers become active in specific developmental and/or environmental contexts are unknown. We exploited inducible p300 binding to chromatin to identify, and then mechanistically dissect, enhancers controlling endotoxin-stimulated gene expression in macrophages. In these enhancers, binding sites for the lineage-restricted and constitutive Ets protein PU.1 coexisted with those for ubiquitous stress-inducible transcription factors such as NF-κB, IRF, and AP-1. PU.1 was required for maintaining H3K4me1 at macrophage-specific enhancers. Reciprocally, ectopic expression of PU.1 reactivated these enhancers in fibroblasts. Thus, the combinatorial assembly of tissue- and signal-specific transcription factors determines the activity of a distinct group of enhancers. We suggest that this may represent a general paradigm in tissue-restricted and stimulus-responsive gene regulation.

Stem cells have become one of the "buzz" topics in the last decade or so. One of the best systems to study adult stem cells in vivo is in the model organism, Drosophila melanogaster. One hundred years of genetic analysis, a sequenced and highly annotated genome and genomics makes this a difficult organism to avoid. The JAK/STAT pathway has been shown to regulate stem cells during haematopoiesis and gametogenesis in Drosophila. In this review we cover the current literature and contrast each group of stem cells with respect to JAK/STAT signaling.

The RAS proto-oncogene Harvey rat sarcoma viral oncogene homolog (HRAS) encodes a small GTPase that transduces signals from cell surface receptors to intracellular effectors to control cellular behavior. Although somatic HRAS mutations have been described in many cancers, germline mutations cause Costello syndrome (CS), a congenital disorder associated with predisposition to malignancy. Based on the epidemiology of CS and the occurrence of HRAS mutations in spermatocytic seminoma, we proposed that activating HRAS mutations become enriched in sperm through a process akin to tumorigenesis, termed selfish spermatogonial selection. To test this hypothesis, we quantified the levels, in blood and sperm samples, of HRAS mutations at the p.G12 codon and compared the results to changes at the p.A11 codon, at which activating mutations do not occur. The data strongly support the role of selection in determining HRAS mutation levels in sperm, and hence the occurrence of CS, but we also found differences from the mutation pattern in tumorigenesis. First, the relative prevalence of mutations in sperm correlates weakly with their in vitro activating properties and occurrence in cancers. Second, specific tandem base substitutions (predominantly GCTT/AA) occur in sperm but not in cancers; genomewide analysis showed that this same mutation is also overrepresented in constitutional pathogenic and polymorphic variants, suggesting a heightened vulnerability to these mutations in the germline. We developed a statistical model to show how both intrinsic mutation rate and selfish selection contribute to the mutational burden borne by the paternal germline.

Improved sequencing technologies offer unprecedented opportunities for investigating the role of rare genetic variation in common disease. However, there are considerable challenges with respect to study design, data analysis and replication. Using pooled next-generation sequencing of 507 genes implicated in the repair of DNA in 1,150 samples, an analytical strategy focused on protein-truncating variants (PTVs) and a large-scale sequencing case-control replication experiment in 13,642 individuals, here we show that rare PTVs in the p53-inducible protein phosphatase PPM1D are associated with predisposition to breast cancer and ovarian cancer. PPM1D PTV mutations were present in 25 out of 7,781 cases versus 1 out of 5,861 controls (P = 1.12 × 10(-5)), including 18 mutations in 6,912 individuals with breast cancer (P = 2.42 × 10(-4)) and 12 mutations in 1,121 individuals with ovarian cancer (P = 3.10 × 10(-9)). Notably, all of the identified PPM1D PTVs were mosaic in lymphocyte DNA and clustered within a 370-base-pair region in the final exon of the gene, carboxy-terminal to the phosphatase catalytic domain. Functional studies demonstrate that the mutations result in enhanced suppression of p53 in response to ionizing radiation exposure, suggesting that the mutant alleles encode hyperactive PPM1D isoforms. Thus, although the mutations cause premature protein truncation, they do not result in the simple loss-of-function effect typically associated with this class of variant, but instead probably have a gain-of-function effect. Our results have implications for the detection and management of breast and ovarian cancer risk. More generally, these data provide new insights into the role of rare and of mosaic genetic variants in common conditions, and the use of sequencing in their identification.

β-III spectrin is present in the brain and is known to be important in the function of the cerebellum. Heterozygous mutations in SPTBN2, the gene encoding β-III spectrin, cause Spinocerebellar Ataxia Type 5 (SCA5), an adult-onset, slowly progressive, autosomal-dominant pure cerebellar ataxia. SCA5 is sometimes known as “Lincoln ataxia,” because the largest known family is descended from relatives of the United States President Abraham Lincoln. Using targeted capture and next-generation sequencing, we identified a homozygous stop codon in SPTBN2 in a consanguineous family in which childhood developmental ataxia co-segregates with cognitive impairment. The cognitive impairment could result from mutations in a second gene, but further analysis using whole-genome sequencing combined with SNP array analysis did not reveal any evidence of other mutations. We also examined a mouse knockout of β-III spectrin in which ataxia and progressive degeneration of cerebellar Purkinje cells has been previously reported and found morphological abnormalities in neurons from prefrontal cortex and deficits in object recognition tasks, consistent with the human cognitive phenotype. These data provide the first evidence that β-III spectrin plays an important role in cortical brain development and cognition, in addition to its function in the cerebellum; and we conclude that cognitive impairment is an integral part of this novel recessive ataxic syndrome, Spectrin-associated Autosomal Recessive Cerebellar Ataxia type 1 (SPARCA1). In addition, the identification of SPARCA1 and normal heterozygous carriers of the stop codon in SPTBN2 provides insights into the mechanism of molecular dominance in SCA5 and demonstrates that the cell-specific repertoire of spectrin subunits underlies a novel group of disorders, the neuronal spectrinopathies, which includes SCA5, SPARCA1, and a form of West syndrome., Author Summary β-III spectrin is present in the brain and is known to be important in the function of the cerebellum. Mutations in β-III spectrin cause spinocerebellar ataxia type 5 (SCA5), sometimes called Lincoln ataxia because it was first described in the relatives of United States President Abraham Lincoln. This is generally an adult-onset progressive cerebellar disorder. Recessive mutations have not previously been described in any of the brain spectrins. We identified a homozygous mutation in SPTBN2, which causes a more severe disorder than SCA5, with a developmental cerebellar ataxia, which is present from childhood; in addition there is marked cognitive impairment. We call this novel condition SPARCA1 (Spectrin-associated Autosomal Recessive Cerebellar Ataxia type 1). This condition could be caused by two separate gene mutations; but we show, using a combination of genome-wide mapping, whole-genome sequencing, and detailed behavioural and neuropathological analysis of a β-III spectrin mouse knockout, that both the ataxia and cognitive impairment are caused by the recessive mutations in β-III spectrin. SPARCA1 is one of a family of neuronal spectrinopathies and illustrates the importance of spectrins in brain development and function.

The basic unit of genome packaging is the nucleosome, and nucleosomes have long been proposed to restrict DNA accessibility both to damage and to transcription. Nucleosome number in cells was considered fixed, but recently aging yeast and mammalian cells were shown to contain fewer nucleosomes. We show here that mammalian cells lacking High Mobility Group Box 1 protein (HMGB1) contain a reduced amount of core, linker, and variant histones, and a correspondingly reduced number of nucleosomes, possibly because HMGB1 facilitates nucleosome assembly. Yeast nhp6 mutants lacking Nhp6a and -b proteins, which are related to HMGB1, also have a reduced amount of histones and fewer nucleosomes. Nucleosome limitation in both mammalian and yeast cells increases the sensitivity of DNA to damage, increases transcription globally, and affects the relative expression of about 10% of genes. In yeast nhp6 cells the loss of more than one nucleosome in four does not affect the location of nucleosomes and their spacing, but nucleosomal occupancy. The decrease in nucleosomal occupancy is non-uniform and can be modelled assuming that different nucleosomal sites compete for available histones. Sites with a high propensity to occupation are almost always packaged into nucleosomes both in wild type and nucleosome-depleted cells; nucleosomes on sites with low propensity to occupation are disproportionately lost in nucleosome-depleted cells. We suggest that variation in nucleosome number, by affecting nucleosomal occupancy both genomewide and gene-specifically, constitutes a novel layer of epigenetic regulation., Author Summary The accurate preservation and correct retrieval of genetic information is crucial for all living organisms. In eukaryotes, whether single-celled yeast or complex mammals, the DNA containing the genetic information is wrapped around beads of histone proteins to form structures called nucleosomes along the length of the DNA; this packaging arrangement helps protect the genome from damage and may restrict access to the genetic information. Until recently, the amount of histones and, consequently, the number of nucleosomes in the cell were considered fixed. Here, we show that in both mammalian and yeast cells that lack a single protein—HMGB1 in mammals or Nhp6a/b in yeast—the abundance of histones and nucleosomes decreases by 20%–30%. Contrary to expectations, we found that in yeast the nucleosomes do not redistribute along DNA when they are fewer: they largely maintain their positions, but the amount of time each specific DNA site spends wrapped in a nucleosome (i.e., its occupancy) decreases. Sequences that are already less frequently occupied than others in normal yeast cells lose disproportionally more nucleosomes in the mutant yeast that lack Nhp6a/b. This gives rise to a global increase in transcription and specific alterations in the expression of certain genes. This study thus contributes to a deeper understanding of how the DNA is packaged and organized. It also suggests that the cell's histone content might contribute in an important way to gene regulation.