The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matte

Evaluation of polygenic risk scores for breast and ovarian cancer risk prediction in BRCA1 and BRCA2 mutation carriers

Background: Genome-wide association studies (GWAS) have identified 94 common single-nucleotide polymorphisms (SNPs) associated with breast cancer (BC) risk and 18 associated with ovarian cancer (OC) risk. Several of these are also associated with risk of BC or OC for women who carry a pathogenic mutation in the high-risk BC and OC genes BRCA1 or BRCA2. The combined effects of these variants on BC or OC risk for BRCA1 and BRCA2 mutation carriers have not yet been assessed while their clinical management could benefit from improved personalized risk estimates. Methods: We constructed polygenic risk scores (PRS) using BC and OC susceptibility SNPs identified through population-based GWAS: for BC (overall, estrogen receptor [ER]-positive, and ER-negative) and for OC. Using data from 15 252 female BRCA1 and 8211 BRCA2 carriers, the association of each PRS with BC or OC risk was evaluated using a weighted cohort approach, with time to diagnosis as the outcome and estimation of the hazard ratios (HRs) per standard deviation increase in the PRS. Results: The PRS for ER-negative BC displayed the strongest association with BC risk in BRCA1 carriers (HR = 1.27, 95% confidence interval [CI] = 1.23 to 1.31, P = 8.2 x 10(53)). In BRCA2 carriers, the strongest association with BC risk was seen for the overall BC PRS (HR = 1.22, 95% CI = 1.17 to 1.28, P = 7.2 x 10(-20)). The OC PRS was strongly associated with OC risk for both BRCA1 and BRCA2 carriers. These translate to differences in absolute risks (more than 10% in each case) between the top and bottom deciles of the PRS distribution; for example, the OC risk was 6% by age 80 years for BRCA2 carriers at the 10th percentile of the OC PRS compared with 19% risk for those at the 90th percentile of PRS. Conclusions: BC and OC PRS are predictive of cancer risk in BRCA1 and BRCA2 carriers. Incorporation of the PRS into risk prediction models has promise to better inform decisions on cancer risk management

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

Background: Most $\textit{BRCA1}$ or $\textit{BRCA2}$ mutation carriers have inherited a single (heterozygous) mutation. Transheterozygotes (TH) who have inherited deleterious mutations in both $\textit{BRCA1}$ and $\textit{BRCA2}$ are rare, and the consequences of transheterozygosity are poorly understood. Methods: From 32,295 female $\textit{BRCA1/2}$ mutation carriers, we identified 93 TH (0.3 %). "Cases" were defined as TH, and "controls" were single mutations at $\textit{BRCA1}$ (SH1) or $\textit{BRCA2}$ (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 $\textit{BRCA1}$ or $\textit{BRCA2}$ 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.ACA and the CIMBA data management are funded by Cancer Research UK (C12292/A20861 and C12292/A11174). TRR was supported by R01-CA083855, R01-CA102776, and P50-CA083638. KLN, TMF, and SMD are supported by the Basser Research Center at the University of Pennsylvania. BP is supported by R01-CA112520. Cancer Research UK provided financial support for this work. ACA is a Senior Cancer Research UK Cancer Research Fellow. DFE is Cancer Research UK Principal Research Fellow. Tumor analysis was funded by STOP CANCER (to SJR). Study-specific acknowledgements are as provided in the manuscript

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

Association of breast cancer risk in BRCA1 and BRCA2 mutation carriers with genetic variants showing differential allelic expression:Identification of a modifier of breast cancer risk at locus 11q22.3

Cis-acting regulatory SNPs resulting in differential allelic expression (DAE) may, in part, explain the underlying phenotypic variation associated with many complex diseases. To investigate whether common variants associated with DAE were involved in breast cancer susceptibility among BRCA1 and BRCA2 mutation carriers, a list of 175 genes was developed based of their involvement in cancer-related pathways.Using data from a genome-wide map of SNPs associated with allelic expression, we assessed the association of similar to 320 SNPs located in the vicinity of these genes with breast and ovarian cancer risks in 15,252 BRCA1 and 8211 BRCA2 mutation carriers ascertained from 54 studies participating in the Consortium of Investigators of Modifiers of BRCA1/2.We identified a region on 11q22.3 that is significantly associated with breast cancer risk in BRCA1 mutation carriers (most significant SNP rs228595 p = 7 x 10(-6)). This association was absent in BRCA2 carriers (p = 0.57). The 11q22.3 region notably encompasses genes such as ACAT1, NPAT, and ATM. Expression quantitative trait loci associations were observed in both normal breast and tumors across this region, namely for ACAT1, ATM, and other genes. In silico analysis revealed some overlap between top risk-associated SNPs and relevant biological features in mammary cell data, which suggests potential functional significance.We identified 11q22.3 as a new modifier locus in BRCA1 carriers. Replication in larger studies using estrogen receptor (ER)-negative or triple-negative (i.e., ER-, progesterone receptor-, and HER2-negative) cases could therefore be helpful to confirm the association of this locus with breast cancer risk.</p

Association of Type and Location of BRCA1 and BRCA2 Mutations With Risk of Breast and Ovarian Cancer (vol 313, pg 1347, 2015)

Heli Nevanlinna ja Kristiina Aittomäki ovat CIMBA Consortium -työryhmän jäseniä.IMPORTANCE Limited information about the relationship between specific mutations in BRCA1 or BRCA2 (BRCA1/2) and cancer risk exists. OBJECTIVE To identify mutation-specific cancer risks for carriers of BRCA1/2. DESIGN, SETTING, AND PARTICIPANTS Observational study of women who were ascertained between 1937 and 2011 (median, 1999) and found to carry disease-associated BRCA1 or BRCA2 mutations. The international sample comprised 19 581 carriers of BRCA1 mutations and 11 900 carriers of BRCA2 mutations from 55 centers in 33 countries on 6 continents. We estimated hazard ratios for breast and ovarian cancer based on mutation type, function, and nucleotide position. We also estimated RHR, the ratio of breast vs ovarian cancer hazard ratios. A value of RHR greater than 1 indicated elevated breast cancer risk; a value of RHR less than 1 indicated elevated ovarian cancer risk. EXPOSURES Mutations of BRCA1 or BRCA2. MAIN OUTCOMES AND MEASURES Breast and ovarian cancer risks. RESULTS Among BRCA1 mutation carriers, 9052 women (46%) were diagnosed with breast cancer, 2317(12%) with ovarian cancer, 1041 (5%) with breast and ovarian cancer, and 7171 (37%) without cancer. Among BRCA2 mutation carriers, 6180 women (52%) were diagnosed with breast cancer, 682(6%) with ovarian cancer, 272(2%) with breast and ovarian cancer, and 4766 (40%) without cancer. In BRCA1, we identified 3 breast cancer cluster regions (BCCRs) located at c.179 to c.505 (BCCR1; RHR = 1.46; 95% Cl, 1.22-1.74; P = 2 x 10(-6)), c.4328 to c.4945 (BCCR2; RH R = 1.34; 95% Cl, 1.01-1.78; P =.04), and c. 5261 to c.5563 (BCCR2', RHR = 1.38; 95% Cl, 1.22-1.55; P = 6 x 10(-9)). We also identified an ovarian cancer cluster region (OCCR) from c.1380 to c.4062 (approximately exon 11) with RHR = 0.62 (95% Cl, 0.56-0.70; P = 9 x 10(-17)). In BRCA2, we observed multiple BCCRs spanning c.1 to c.596 (BCCR1; RHR = 1.71; 95% Cl, 1.06-2.78; P =.03), c.772 to c.1806 (BCCRI; RHR = 1.63; 95% Cl, 1.10-2.40; P =.01), and c.7394 to c.8904 (BCCR2; RHR = 2.31; 95% Cl, 1.69-3.16; P =.00002). We also identified 3 OCCRs: the first (OCCR1) spanned c.3249 to c.5681 that was adjacent to c.5946delT (6174delT; RHR = 0.51; 95% Cl, 0.44-0.60; P = 6 x 10(-17)). The second OCCR spanned c.6645 to c.7471 (OCCR2; RHR = 0.57; 95% Cl, 0.41-0.80; P =.001). Mutations conferring nonsense-mediated decay were associated with differential breast or ovarian cancer risks and an earlier age of breast cancer diagnosis for both BRCA1 and BRCA2 mutation carriers. CONCLUSIONS AND RELEVANCE Breast and ovarian cancer risks varied by type and location of BRCA1/2 mutations. With appropriate validation, these data may have implications for risk assessment and cancer prevention decision making for carriers of BRCA1 and BRCA2 mutations.Peer reviewe

Identification of six new susceptibility loci for invasive epithelial ovarian cancer.

Genome-wide association studies (GWAS) have identified 12 epithelial ovarian cancer (EOC) susceptibility alleles. The pattern of association at these loci is consistent in BRCA1 and BRCA2 mutation carriers who are at high risk of EOC. After imputation to 1000 Genomes Project data, we assessed associations of 11 million genetic variants with EOC risk from 15,437 cases unselected for family history and 30,845 controls and from 15,252 BRCA1 mutation carriers and 8,211 BRCA2 mutation carriers (3,096 with ovarian cancer), and we combined the results in a meta-analysis. This new study design yielded increased statistical power, leading to the discovery of six new EOC susceptibility loci. Variants at 1p36 (nearest gene, WNT4), 4q26 (SYNPO2), 9q34.2 (ABO) and 17q11.2 (ATAD5) were associated with EOC risk, and at 1p34.3 (RSPO1) and 6p22.1 (GPX6) variants were specifically associated with the serous EOC subtype, all with P < 5 × 10(-8). Incorporating these variants into risk assessment tools will improve clinical risk predictions for BRCA1 and BRCA2 mutation carriers.COGS project is funded through a European Commission's Seventh Framework Programme grant (agreement number 223175 ] HEALTH ]F2 ]2009 ]223175). The CIMBA data management and data analysis were supported by Cancer Research.UK grants 12292/A11174 and C1287/A10118. The Ovarian Cancer Association Consortium is supported by a grant from the Ovarian Cancer Research Fund thanks to donations by the family and friends of Kathryn Sladek Smith (PPD/RPCI.07). The scientific development and funding for this project were in part supported by the US National Cancer Institute GAME ]ON Post ]GWAS Initiative (U19 ]CA148112). This study made use of data generated by the Wellcome Trust Case Control consortium. Funding for the project was provided by the Wellcome Trust under award 076113. The results published here are in part based upon data generated by The Cancer Genome Atlas Pilot Project established by the National Cancer Institute and National Human Genome Research Institute (dbGap accession number phs000178.v8.p7). The cBio portal is developed and maintained by the Computational Biology Center at Memorial Sloan ] Kettering Cancer Center. SH is supported by an NHMRC Program Grant to GCT. Details of the funding of individual investigators and studies are provided in the Supplementary Note. This study made use of data generated by the Wellcome Trust Case Control consortium, funding for which was provided by the Wellcome Trust under award 076113. The results published here are, in part, based upon data generated by The Cancer Genome Atlas Pilot Project established by the National Cancerhttp://dx.doi.org/10.1038/ng.3185This is the Author Accepted Manuscript of 'Identification of six new susceptibility loci for invasive epithelial ovarian cancer' which was published in Nature Genetics 47, 164–171 (2015) © Nature Publishing Group - content may only be used for academic research

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers

Introduction: Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. Methods: We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. Results: We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. Conclusions: This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects.Peer reviewe