A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes.

Chronic kidney disease (CKD), impairment of kidney function, is a serious public health problem, and the assessment of genetic factors influencing kidney function has substantial clinical relevance. Here, we report a meta-analysis of genome-wide association studies for kidney function-related traits, including 71,149 east Asian individuals from 18 studies in 11 population-, hospital- or family-based cohorts, conducted as part of the Asian Genetic Epidemiology Network (AGEN). Our meta-analysis identified 17 loci newly associated with kidney function-related traits, including the concentrations of blood urea nitrogen, uric acid and serum creatinine and estimated glomerular filtration rate based on serum creatinine levels (eGFRcrea) (P < 5.0 × 10(-8)). We further examined these loci with in silico replication in individuals of European ancestry from the KidneyGen, CKDGen and GUGC consortia, including a combined total of ∼110,347 individuals. We identify pleiotropic associations among these loci with kidney function-related traits and risk of CKD. These findings provide new insights into the genetics of kidney function.

Rationale

Therapies that inhibit CETP (cholesteryl ester transfer protein) have failed to demonstrate a reduction in risk for coronary heart disease (CHD). Human DNA sequence variants that truncate the CETP gene may provide insight into the efficacy of CETP inhibition.

Objective

To test whether protein-truncating variants (PTVs) at the CETP gene were associated with plasma lipid levels and CHD.

Methods and results

We sequenced the exons of the CETP gene in 58 469 participants from 12 case-control studies (18 817 CHD cases, 39 652 CHD-free controls). We defined PTV as those that lead to a premature stop, disrupt canonical splice sites, or lead to insertions/deletions that shift frame. We also genotyped 1 Japanese-specific PTV in 27561 participants from 3 case-control studies (14 286 CHD cases, 13 275 CHD-free controls). We tested association of CETP PTV carrier status with both plasma lipids and CHD. Among 58 469 participants with CETP gene-sequencing data available, average age was 51.5 years and 43% were women; 1 in 975 participants carried a PTV at the CETP gene. Compared with noncarriers, carriers of PTV at CETP had higher high-density lipoprotein cholesterol (effect size, 22.6 mg/dL; 95% confidence interval, 18-27; P<1.0×10^-4), lower low-density lipoprotein cholesterol (-12.2 mg/dL; 95% confidence interval, -23 to -0.98; P=0.033), and lower triglycerides (-6.3%; 95% confidence interval, -12 to -0.22; P=0.043). CETP PTV carrier status was associated with reduced risk for CHD (summary odds ratio, 0.70; 95% confidence interval, 0.54-0.90; P=5.1×10^-3).

Conclusions

Compared with noncarriers, carriers of PTV at CETP displayed higher high-density lipoprotein cholesterol, lower low-density lipoprotein cholesterol, lower triglycerides, and lower risk for CHD.

Glycated hemoglobin A1c (HbA1c) is used as a measure of glycemic control and also as a diagnostic criterion for diabetes. To discover novel loci harboring common variants associated with HbA1c in East Asians, we conducted a meta-analysis of 13 genome-wide association studies (GWAS; N = 21,026). We replicated our findings in three additional studies comprising 11,576 individuals of East Asian ancestry. Ten variants showed associations that reached genome-wide significance in the discovery data set, of which nine (four novel variants at TMEM79 [P value = 1.3 × 10(-23)], HBS1L/MYB [8.5 × 10(-15)], MYO9B [9.0 × 10(-12)], and CYBA [1.1 × 10(-8)] as well as five variants at loci that had been previously identified [CDKAL1, G6PC2/ABCB11, GCK, ANK1, and FN3KI]) showed consistent evidence of association in replication data sets. These variants explained 1.76% of the variance in HbA1c. Several of these variants (TMEM79, HBS1L/MYB, CYBA, MYO9B, ANK1, and FN3K) showed no association with either blood glucose or type 2 diabetes. Among individuals with nondiabetic levels of fasting glucose (<7.0 mmol/L) but elevated HbA1c (≥6.5%), 36.1% had HbA1c <6.5% after adjustment for these six variants. Our East Asian GWAS meta-analysis has identified novel variants associated with HbA1c as well as demonstrated that the effects of known variants are largely transferable across ethnic groups. Variants affecting erythrocyte parameters rather than glucose metabolism may be relevant to the use of HbA1c for diagnosing diabetes in these populations.

Glycated hemoglobin A1c (HbA1c) is used as a measure of glycemic control and also as a diagnostic criterion for diabetes. To discover novel loci harboring common variants associated with HbA1c in East Asians, we conducted a meta-analysis of 13 genome-wide association studies (GWAS; N = 21,026). We replicated our findings in three additional studies comprising 11,576 individuals of East Asian ancestry. Ten variants showed associations that reached genome-wide significance in the discovery data set, of which nine (four novel variants at TMEM79 [P value = 1.3 × 10(-23)], HBS1L/MYB [8.5 × 10(-15)], MYO9B [9.0 × 10(-12)], and CYBA [1.1 × 10(-8)] as well as five variants at loci that had been previously identified [CDKAL1, G6PC2/ABCB11, GCK, ANK1, and FN3KI]) showed consistent evidence of association in replication data sets. These variants explained 1.76% of the variance in HbA1c. Several of these variants (TMEM79, HBS1L/MYB, CYBA, MYO9B, ANK1, and FN3K) showed no association with either blood glucose or type 2 diabetes. Among individuals with nondiabetic levels of fasting glucose (<7.0 mmol/L) but elevated HbA1c (≥6.5%), 36.1% had HbA1c <6.5% after adjustment for these six variants. Our East Asian GWAS meta-analysis has identified novel variants associated with HbA1c as well as demonstrated that the effects of known variants are largely transferable across ethnic groups. Variants affecting erythrocyte parameters rather than glucose metabolism may be relevant to the use of HbA1c for diagnosing diabetes in these populations.

Sixty genetic loci associated with abdominal obesity, measured by waist circumference (WC) and waist-hip ratio (WHR), have been previously identified, primarily from studies conducted in European-ancestry populations. We conducted a meta-analysis of associations of abdominal obesity with approximately 2.5 million single nucleotide polymorphisms (SNPs) among 53,052 (for WC) and 48,312 (for WHR) individuals of Asian descent, and replicated 33 selected SNPs among 3,762 to 17,110 additional individuals. We identified four novel loci near the EFEMP1, ADAMTSL3 , CNPY2, and GNAS genes that were associated with WC after adjustment for body mass index (BMI); two loci near the NID2 and HLA-DRB5 genes associated with WHR after adjustment for BMI, and three loci near the CEP120, TSC22D2, and SLC22A2 genes associated with WC without adjustment for BMI. Functional enrichment analyses revealed enrichment of corticotropin-releasing hormone signaling, GNRH signaling, and/or CDK5 signaling pathways for those newly-identified loci. Our study provides additional insight on genetic contribution to abdominal obesity.

Human height is associated with risk of multiple diseases and is profoundly determined by an individual's genetic makeup and shows a high degree of ethnic heterogeneity. Large-scale genome-wide association (GWA) analyses of adult height in Europeans have identified nearly 180 genetic loci. A recent study showed high replicability of results from Europeans-based GWA studies in Asians; however, population-specific loci may exist due to distinct linkage disequilibrium patterns. We carried out a GWA meta-analysis in 93 926 individuals from East Asia. We identified 98 loci, including 17 novel and 81 previously reported loci, associated with height at P < 5 × 10(-8), together explaining 8.89% of phenotypic variance. Among the newly identified variants, 10 are commonly distributed (minor allele frequency, MAF > 5%) in Europeans, with comparable frequencies with in Asians, and 7 single-nucleotide polymorphisms are with low frequency (MAF < 5%) in Europeans. In addition, our data suggest that novel biological pathway such as the protein tyrosine phosphatase family is involved in regulation of height. The findings from this study considerably expand our knowledge of the genetic architecture of human height in Asians.

Recent genetic association studies have identified 55 genetic loci associated with obesity or body mass index (BMI). The vast majority, 51 loci, however, were identified in European-ancestry populations. We conducted a meta-analysis of associations between BMI and ∼2.5 million genotyped or imputed single nucleotide polymorphisms among 86 757 individuals of Asian ancestry, followed by in silico and de novo replication among 7488-47 352 additional Asian-ancestry individuals. We identified four novel BMI-associated loci near the KCNQ1 (rs2237892, P = 9.29 × 10(-13)), ALDH2/MYL2 (rs671, P = 3.40 × 10(-11); rs12229654, P = 4.56 × 10(-9)), ITIH4 (rs2535633, P = 1.77 × 10(-10)) and NT5C2 (rs11191580, P = 3.83 × 10(-8)) genes. The association of BMI with rs2237892, rs671 and rs12229654 was significantly stronger among men than among women. Of the 51 BMI-associated loci initially identified in European-ancestry populations, we confirmed eight loci at the genome-wide significance level (P < 5.0 × 10(-8)) and an additional 14 at P < 1.0 × 10(-3) with the same direction of effect as reported previously. Findings from this analysis expand our knowledge of the genetic basis of obesity.

Meta-analyses of genome-wide association studies (GWAS) have identified more than 240 loci that are associated with type 2 diabetes (T2D)^1,2; however, most of these loci have been identified in analyses of individuals with European ancestry. Here, to examine T2D risk in East Asian individuals, we carried out a meta-analysis of GWAS data from 77,418 individuals with T2D and 356,122 healthy control individuals. In the main analysis, we identified 301 distinct association signals at 183 loci, and across T2D association models with and without consideration of body mass index and sex, we identified 61 loci that are newly implicated in predisposition to T2D. Common variants associated with T2D in both East Asian and European populations exhibited strongly correlated effect sizes. Previously undescribed associations include signals in or near GDAP1, PTF1A, SIX3, ALDH2, a microRNA cluster, and genes that affect the differentiation of muscle and adipose cells³. At another locus, expression quantitative trait loci at two overlapping T2D signals affect two genes-NKX6-3 and ANK1-in different tissues^4-6. Association studies in diverse populations identify additional loci and elucidate disease-associated genes, biology, and pathways.

Recent genetic association studies have identified 55 genetic loci associated with obesity or body mass index (BMI). The vast majority, 51 loci, however, were identified in European-ancestry populations. We conducted a meta-analysis of associations between BMI and ∼2.5 million genotyped or imputed single nucleotide polymorphisms among 86 757 individuals of Asian ancestry, followed by in silico and de novo replication among 7488-47 352 additional Asian-ancestry individuals. We identified four novel BMI-associated loci near the KCNQ1 (rs2237892, P = 9.29 × 10(-13)), ALDH2/MYL2 (rs671, P = 3.40 × 10(-11); rs12229654, P = 4.56 × 10(-9)), ITIH4 (rs2535633, P = 1.77 × 10(-10)) and NT5C2 (rs11191580, P = 3.83 × 10(-8)) genes. The association of BMI with rs2237892, rs671 and rs12229654 was significantly stronger among men than among women. Of the 51 BMI-associated loci initially identified in European-ancestry populations, we confirmed eight loci at the genome-wide significance level (P < 5.0 × 10(-8)) and an additional 14 at P < 1.0 × 10(-3) with the same direction of effect as reported previously. Findings from this analysis expand our knowledge of the genetic basis of obesity.