The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses of Dirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.     

Structures of APC/C(Cdh1) with substrates identify Cdh1 and Apc10 as the D-box co-receptor

The ubiquitylation of cell-cycle regulatory proteins by the large multimeric anaphase-promoting complex (APC/C) controls sister chromatid segregation and the exit from mitosis. Selection of APC/C targets is achieved through recognition of destruction motifs, predominantly the destruction (D)-box and KEN (Lys-Glu-Asn)-box. Although this process is known to involve a co-activator protein (either Cdc20 or Cdh1) together with core APC/C subunits, the structural basis for substrate recognition and ubiquitylation is not understood. Here we investigate budding yeast APC/C using single-particle electron microscopy and determine a cryo-electron microscopy map of APC/C in complex with the Cdh1 co-activator protein (APC/C(Cdh1)) bound to a D-box peptide at ～10 ? resolution. We find that a combined catalytic and substrate-recognition module is located within the central cavity of the APC/C assembled from Cdh1, Apc10--a core APC/C subunit previously implicated in substrate recognition--and the cullin domain of Apc2. Cdh1 and Apc10, identified from difference maps, create a co-receptor for the D-box following repositioning of Cdh1 towards Apc10. Using NMR spectroscopy we demonstrate specific D-box-Apc10 interactions, consistent with a role for Apc10 in directly contributing towards D-box recognition by the APC/C(Cdh1) complex. Our results rationalize the contribution of both co-activator and core APC/C subunits to D-box recognition and provide a structural framework for understanding mechanisms of substrate recognition and catalysis by the APC/C.     

Prion protein cleavage fragments regulate adult neural stem cell quiescence through redox modulation of mitochondrial fission and SOD2 expression

Neurogenesis continues in the post-developmental brain throughout life. The ability to stimulate the production of new neurones requires both quiescent and actively proliferating pools of neural stem cells (NSCs). Actively proliferating NSCs ensure that neurogenic demand can be met, whilst the quiescent pool makes certain NSC reserves do not become depleted. The processes preserving the NSC quiescent pool are only just beginning to be defined. Herein, we identify a switch between NSC proliferation and quiescence through changing intracellular redox signalling. We show that N-terminal post-translational cleavage products of the prion protein (PrP) induce a quiescent state, halting NSC cellular growth, migration, and neurite outgrowth. Quiescence is initiated by the PrP cleavage products through reducing intracellular levels of reactive oxygen species. First, inhibition of redox signalling results in increased mitochondrial fission, which rapidly signals quiescence. Thereafter, quiescence is maintained through downstream increases in the expression and activity of superoxide dismutase-2 that reduces mitochondrial superoxide. We further observe that PrP is predominantly cleaved in quiescent NSCs indicating a homeostatic role for this cascade. Our findings provide new insight into the regulation of NSC quiescence, which potentially could influence brain health throughout adult life.     

Common variants near MC4R are associated with fat mass, weight and risk of obesity

To identify common variants influencing body mass index (BMI), we analyzed genome-wide association data from 16,876 individuals of European descent. After previously reported variants in FTO, the strongest association signal (rs17782313, P = 2.9 x 10(-6)) mapped 188 kb downstream of MC4R (melanocortin-4 receptor), mutations of which are the leading cause of monogenic severe childhood-onset obesity. We confirmed the BMI association in 60,352 adults (per-allele effect = 0.05 Z-score units; P = 2.8 x 10(-15)) and 5,988 children aged 7-11 (0.13 Z-score units; P = 1.5 x 10(-8)). In case-control analyses (n = 10,583), the odds for severe childhood obesity reached 1.30 (P = 8.0 x 10(-11)). Furthermore, we observed overtransmission of the risk allele to obese offspring in 660 families (P (pedigree disequilibrium test average; PDT-avg) = 2.4 x 10(-4)). The SNP location and patterns of phenotypic associations are consistent with effects mediated through altered MC4R function. Our findings establish that common variants near MC4R influence fat mass, weight and obesity risk at the population level and reinforce the need for large-scale data integration to identify variants influencing continuous biomedical traits.     

SLC2A9 is a newly identified urate transporter influencing serum urate concentration, urate excretion and gout

Uric acid is the end product of purine metabolism in humans and great apes, which have lost hepatic uricase activity, leading to uniquely high serum uric acid concentrations (200-500 microM) compared with other mammals (3-120 microM). About 70% of daily urate disposal occurs via the kidneys, and in 5-25% of the human population, impaired renal excretion leads to hyperuricemia. About 10% of people with hyperuricemia develop gout, an inflammatory arthritis that results from deposition of monosodium urate crystals in the joint. We have identified genetic variants within a transporter gene, SLC2A9, that explain 1.7-5.3% of the variance in serum uric acid concentrations, following a genome-wide association scan in a Croatian population sample. SLC2A9 variants were also associated with low fractional excretion of uric acid and/or gout in UK, Croatian and German population samples. SLC2A9 is a known fructose transporter, and we now show that it has strong uric acid transport activity in Xenopus laevis oocytes.     

Genomic surveys by methylation-sensitive SNP analysis identify sequence-dependent allele-specific DNA methylation

Allele-specific DNA methylation (ASM) is a hallmark of imprinted genes, but ASM in the larger nonimprinted fraction of the genome is less well characterized. Using methylation-sensitive SNP analysis (MSNP), we surveyed the human genome at 50K and 250K resolution, identifying ASM as recurrent genotype call conversions from heterozygosity to homozygosity when genomic DNAs were predigested with the methylation-sensitive restriction enzyme HpaII. Using independent assays, we confirmed ASM at 16 SNP-tagged loci distributed across various chromosomes. At 12 of these loci (75%), the ASM tracked strongly with the sequence of adjacent SNPs. Further analysis showed allele-specific mRNA expression at two loci from this methylation-based screen--the vanin and CYP2A6-CYP2A7 gene clusters--both implicated in traits of medical importance. This recurrent phenomenon of sequence-dependent ASM has practical implications for mapping and interpreting associations of noncoding SNPs and haplotypes with human phenotypes.     

Conditional and joint multiple-SNP analysis of GWAS summary statistics identifies additional variants influencing complex traits

We present an approximate conditional and joint association analysis that can use summary-level statistics from a meta-analysis of genome-wide association studies (GWAS) and estimated linkage disequilibrium (LD) from a reference sample with individual-level genotype data. Using this method, we analyzed meta-analysis summary data from the GIANT Consortium for height and body mass index (BMI), with the LD structure estimated from genotype data in two independent cohorts. We identified 36 loci with multiple associated variants for height (38 leading and 49 additional SNPs, 87 in total) via a genome-wide SNP selection procedure. The 49 new SNPs explain approximately 1.3% of variance, nearly doubling the heritability explained at the 36 loci. We did not find any locus showing multiple associated SNPs for BMI. The method we present is computationally fast and is also applicable to case-control data, which we demonstrate in an example from meta-analysis of type 2 diabetes by the DIAGRAM Consortium.     

Common variants at MS4A4/MS4A6E, CD2AP, CD33 and EPHA1 are associated with late-onset Alzheimer's disease

The Alzheimer Disease Genetics Consortium (ADGC) performed a genome-wide association study of late-onset Alzheimer disease using a three-stage design consisting of a discovery stage (stage 1) and two replication stages (stages 2 and 3). Both joint analysis and meta-analysis approaches were used. We obtained genome-wide significant results at MS4A4A (rs4938933; stages 1 and 2, meta-analysis P (P(M)) = 1.7 × 10(-9), joint analysis P (P(J)) = 1.7 × 10(-9); stages 1, 2 and 3, P(M) = 8.2 × 10(-12)), CD2AP (rs9349407; stages 1, 2 and 3, P(M) = 8.6 × 10(-9)), EPHA1 (rs11767557; stages 1, 2 and 3, P(M) = 6.0 × 10(-10)) and CD33 (rs3865444; stages 1, 2 and 3, P(M) = 1.6 × 10(-9)). We also replicated previous associations at CR1 (rs6701713; P(M) = 4.6 × 10(-10), P(J) = 5.2 × 10(-11)), CLU (rs1532278; P(M) = 8.3 × 10(-8), P(J) = 1.9 × 10(-8)), BIN1 (rs7561528; P(M) = 4.0 × 10(-14), P(J) = 5.2 × 10(-14)) and PICALM (rs561655; P(M) = 7.0 × 10(-11), P(J) = 1.0 × 10(-10)), but not at EXOC3L2, to late-onset Alzheimer's disease susceptibility.