Uniqueness and Non-uniqueness in the Einstein Constraints

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte

Inheritance of deleterious mutations at both BRCA1 and BRCA2 in an international sample of 32,295 women

Background: Most BRCA1 or BRCA2 mutation carriers have inherited a single (heterozygous) mutation. Transheterozygotes (TH) who have inherited deleterious mutations in both BRCA1 and BRCA2 are rare, and the consequences of transheterozygosity are poorly understood. Methods: From 32,295 female BRCA1/2 mutation carriers, we identified 93 TH (0.3 %). "Cases" were defined as TH, and "controls" were single mutations at BRCA1 (SH1) or BRCA2 (SH2). Matched SH1 "controls" carried a BRCA1 mutation found in the TH "case". Matched SH2 "controls" carried a BRCA2 mutation found in the TH "case". After matching the TH carriers with SH1 or SH2, 91 TH were matched to 9316 SH1, and 89 TH were matched to 3370 SH2. Results: The majority of TH (45.2 %) involved the three common Jewish mutations. TH were more likely than SH1 and SH2 women to have been ever diagnosed with breast cancer (BC; p = 0.002). TH were more likely to be diagnosed with ovarian cancer (OC) than SH2 (p = 0.017), but not SH1. Age at BC diagnosis was the same in TH vs. SH1 (p = 0.231), but was on average 4.5 years younger in TH than in SH2 (p < 0.001). BC in TH was more likely to be estrogen receptor (ER) positive (p = 0.010) or progesterone receptor (PR) positive (p = 0.013) than in SH1, but less likely to be ER positive (p < 0.001) or PR positive (p = 0.012) than SH2. Among 15 tumors from TH patients, there was no clear pattern of loss of heterozygosity (LOH) for BRCA1 or BRCA2 in either BC or OC. Conclusions: Our observations suggest that clinical TH phenotypes resemble SH1. However, TH breast tumor marker characteristics are phenotypically intermediate to SH1 and SH2

Male breast cancer in BRCA1 and BRCA2 mutation carriers : pathology data from the Consortium of Investigators of Modifiers of BRCA1/2

Background: BRCA1 and, more commonly, BRCA2 mutations are associated with increased risk of male breast cancer (MBC). However, only a paucity of data exists on the pathology of breast cancers (BCs) in men with BRCA1/2 mutations. Using the largest available dataset, we determined whether MBCs arising in BRCA1/2 mutation carriers display specific pathologic features and whether these features differ from those of BRCA1/2 female BCs (FBCs). Methods: We characterised the pathologic features of 419 BRCA1/2 MBCs and, using logistic regression analysis, contrasted those with data from 9675 BRCA1/2 FBCs and with population-based data from 6351 MBCs in the Surveillance, Epidemiology, and End Results (SEER) database. Results: Among BRCA2 MBCs, grade significantly decreased with increasing age at diagnosis (P = 0.005). Compared with BRCA2 FBCs, BRCA2 MBCs were of significantly higher stage (P for trend = 2 x 10(-5)) and higher grade (P for trend = 0.005) and were more likely to be oestrogen receptor-positive [odds ratio (OR) 10.59; 95 % confidence interval (CI) 5.15-21.80] and progesterone receptor-positive (OR 5.04; 95 % CI 3.17-8.04). With the exception of grade, similar patterns of associations emerged when we compared BRCA1 MBCs and FBCs. BRCA2 MBCs also presented with higher grade than MBCs from the SEER database (P for trend = 4 x 10(-12)). Conclusions: On the basis of the largest series analysed to date, our results show that BRCA1/2 MBCs display distinct pathologic characteristics compared with BRCA1/2 FBCs, and we identified a specific BRCA2-associated MBC phenotype characterised by a variable suggesting greater biological aggressiveness (i.e., high histologic grade). These findings could lead to the development of gender-specific risk prediction models and guide clinical strategies appropriate for MBC management.Peer reviewe

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

Structure of mitochondrial poly A RNA polymerase reveals the structural basis for dimerization, ATP selectivity and the SPAX4 disease phenotype

Polyadenylation, performed by poly(A) polymerases (PAPs), is a ubiquitous post-transcriptional modification that plays key roles in multiple aspects of RNA metabolism. Although cytoplasmic and nuclear PAPs have been studied extensively, the mechanism by which mitochondrial PAP (mtPAP) selects adenosine triphosphate over other nucleotides is unknown. Furthermore, mtPAP is unique because it acts as a dimer. However, mtPAP's dimerization requirement remains enigmatic. Here, we show the structural basis for mtPAP's nucleotide selectivity, dimerization and catalysis. Our structures reveal an intricate dimerization interface that features an RNA-recognition module formed through strand complementation. Further, we propose the structural basis for the N478D mutation that drastically reduces the length of poly(A) tails on mitochondrial mRNAs in patients with spastic ataxia 4 (SPAX4), a severe and progressive neurodegenerative disease

X ray structure of tRNA pseudouridine synthase TruD reveals an inserted domain with a novel fold

Pseudouridine synthases catalyse the isomerisation of uridine to pseudouridine in structural RNA. The pseudouridine synthase TruD, that modifies U13 in tRNA, belongs to a recently identified and large family of pseudouridine synthases present in all kingdoms of life. We report here the crystal structure of Escherichia coli TruD at 2.0 resolution. The structure reveals an overall V shaped molecule with an RNA binding cleft formed between two domains a catalytic domain and an insertion domain. The catalytic domain has a fold similar to that of the catalytic domains of previously characterised pseudouridine synthases, whereas the insertion domain displays a novel fol

X ray structure of tRNA pseudouridine synthase TruD reveals an inserted domain with a novel fold

Pseudouridine synthases catalyse the isomerisation of uridine to pseudouridine in structural RNA. The pseudouridine synthase TruD, that modifies U13 in tRNA, belongs to a recently identified and large family of pseudouridine synthases present in all kingdoms of life. We report here the crystal structure of Escherichia coli TruD at 2.0 resolution. The structure reveals an overall V shaped molecule with an RNA binding cleft formed between two domains a catalytic domain and an insertion domain. The catalytic domain has a fold similar to that of the catalytic domains of previously characterised pseudouridine synthases, whereas the insertion domain displays a novel fol