{'fraction_non_alphanumeric': 0.03812959818902094, 'fraction_numerical': 0.04084135068854933, 'mean_word_length': 4.656041611096293, 'pattern_counts': {'":': 0, '<': 23, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 2, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Genome-wide association analyses identify 143 risk variants and putative regulatory mechanisms for type 2 diabetes

Type 2 diabetes (T2D) is a very common disease in humans. Here we conduct a meta-analysis of genome-wide association studies (GWAS) with ~16 million genetic variants in 62,892 T2D cases and 596,424 controls of European ancestry. We identify 139 common and 4 rare variants associated with T2D, 42 of which (39 common and 3 rare variants) are independent of the known variants. Integration of the gene expression data from blood (n = 14,115 and 2765) with the GWAS results identifies 33 putative functional genes for T2D, 3 of which were targeted by approved drugs. A further integration of DNA methylation (n = 1980) and epigenomic annotation data highlight 3 genes (CAMK1D, TP53INP1, and ATP5G1) with plausible regulatory mechanisms, whereby a genetic variant exerts an effect on T2D through epigenetic regulation of gene expression. Our study uncovers additional loci, proposes putative genetic regulatory mechanisms for T2D, and provides evidence of purifying selection for T2D-associated variants.

T ype 2 diabetes (T2D) is a common disease with a worldwide prevalence that increased rapidly from 4.7% in 1980 to 8.5% in 2014 1 . It is primarily caused by insulin resistance (failure of the body's normal response to insulin) and/or insufficient insulin production by beta cells 2 . Genetic studies using linkage analysis and candidate gene approaches have led to the discovery of an initial set of T2D-associated loci (e.g., PPARG and TCF7L2) 3,4 . Over the past decade, genome-wide association studies (GWAS) with increasing sample sizes have identified 144 genetic variants (not completely independent) at 129 loci associated with T2D 5,6 .
Despite a large number of variants discovered using GWAS, the associated variants in total, explains only a small proportion (~10%) of the heritability of T2D 7 . This well-known "missing heritability" problem is likely due to the presence of common variants (minor allele frequencies or MAF ≥ 0.01) that have small effects and have not yet been detected and/or rare variants that are not well tagged by common single nucleotide polymorphisms (SNPs) 7 . The contribution of rare variants to genetic variation in the occurrence of common diseases is under debate 8 , and a recent study suggested that the contribution of rare variants to the heritability of T2D is likely to be limited 9 . If most T2D-associated genetic variants are common in the population, continual discoveries of variants with small effects are expected from largescale GWAS using the current experimental design. Furthermore, limited progress has been made in understanding the regulatory mechanisms of the genetic loci identified by GWAS. Thus, the etiology and the genetic basis underlying the development of this disease remain largely unknown. Recent methodological advances have provided us with an opportunity to identify functional genes and their regulatory elements by combining GWAS summary statistics with data from molecular quantitative trait loci studies with large sample sizes 10,11 .
In this study, we perform a meta-analysis of GWAS in a very large sample of T2D (62,892 cases and 596,424 controls), by combining 3 GWAS data sets of European ancestry: DIAbetes Genetics Replication and Meta-analysis (DIAGRAM) 5 , Genetic Epidemiology Research on Aging (GERA) 12 , and the full cohort release of the UK Biobank (UKB) 13 . We then integrate the GWAS meta-analysis results with gene expression and DNA methylation data to identify genes that might be functionally relevant to T2D and to infer plausible mechanisms, whereby genetic variants affect T2D risk through gene regulation by DNA methylation 11 . We further estimate the genetic architecture of T2D using wholegenome estimation approaches. Our study identifies additional T2D-risk variants, prioritizes functional genes, and proposes putative genetic regulatory mechanisms for T2D.

Results
Meta-analysis identifies 39 previously unknown loci. We metaanalyzed 5,053,015 genotyped or imputed autosomal SNPs (MAF ≥ 0.01) in 62,892 T2D cases and 596,424 controls from the DIAGRAM (12,171 cases vs. 56,862 controls in stage 1 and 22,669 cases vs. 58,119 controls in stage 2), GERA (6905 cases and 46,983 controls) and UKB (21,147 cases and 434,460 controls) data sets after quality controls (Supplementary Fig. 1 and Methods). Summary statistics in DIAGRAM were imputed to the 1000 Genomes Project 14 (1KGP) phase 1 using a summary databased imputation approach, ImpG 15 (Supplementary Note 1), and we used an inverse-variance method 16 to meta-analyze the imputed DIAGRAM data with the summary data from GWAS analyses of GERA and UKB (Methods and Fig. 1a). We demonstrated by linkage disequilibrium (LD) score regression analysis 17,18 that the inflation in test statistics due to population structure was negligible in each data set, and there was no  Four loci with P < 5 × 10 −9 are highlighted in red. The blue lines denote the genome-wide significant threshold of P < 5 × 10 −8 , and the red lines denote a more stringent threshold of P < 5 × 10 −9 evidence of sample overlap among the 3 data sets (Supplementary Note 2 and Supplementary Table 1). The mean χ 2 statistic was 1.685. LD score regression analysis of the meta-analysis summary statistics showed an estimate of SNP-based heritabilitŷ h 2 SNP on the liability scale of 0.196 (s.e. = 0.011) and an estimate of intercept of 1.049 (s.e. = 0.014), consistent with a model in which the genomic inflation in test statistics is driven by polygenic effects 17 . After clumping the SNPs using LD information from the UKB genotypes (clumping r 2 threshold = 0.01 and window size = 1 Mb), there were 139 nearindependent variants at P < 5 × 10 −8 (Supplementary Data 1). All of the loci previously reported by DIAGRAM were still genome-wide significant in our meta-analysis results. The most significant association was at rs7903146 (P = 1.3 × 10 −347 ) at the known TCF7L2 locus 4,19 . Among the 139 variants, 39 are not in LD with the known variants ( Fig. 1 and Table 1). The result remained unchanged when the GERA cohort was imputed to Haplotype Reference Consortium (HRC) (Supplementary Fig. 2). We regarded these 39 variants as novel discoveries; more than half of them passed a more stringent significance threshold at P < 1 × 10 −8 (Table 1), a conservative control of genome-wide false-positive rate (GWFPR) suggested by a recent simulation study 20 . The functional relevance of some novel gene loci to the disease was supported by existing biological or molecular evidence related to insulin and glucose (Supplementary Note 3). Forest plots showed that the effect directions of the 39 novel loci were consistent across the 3 GWAS data sets ( Supplementary  Fig. 3). Regional association plots showed that some loci have complicated LD structures, and it is largely unclear which genes are responsible for the observed SNP-T2D associations ( Supplementary Fig. 4). We also performed gene-based analysis by GCTA-fastBAT 21 , and conditional analysis by GCTA-COJO 22 , and discovered 4 loci with multiple independent signals associated with T2D (Supplementary Notes 4  Of all the 139 T2D-associated loci identified in our metaanalysis, 16 and 25 were significant in insulin secretion and sensitivity GWAS, respectively, from the MAGIC consortium 24,25 (see URLs section) after correcting for multiple tests (i.e., 0.05/ 139), with only 1 locus showing significant associations with both insulin secretion and sensitivity. The limited number of overlapping associations observed might be due to the relatively small sample sizes in the insulin studies. We further estimated the genetic correlation (r g ) between insulin secretion (or sensitivity) and T2D by the bivariate LD score regression approach 18 using summary-level data. The estimate of r g between T2D and insulin secretion was −0.15 (s.e. = 0.10), and that between T2D and insulin sensitivity was −0.57 (s.e. = 0.10). Gene set enrichment test also showed that T2D-associated loci were enriched in "glucose homeostasis" and "insulin secretion" pathways (Supplementary Note 7, Supplementary Fig. 8, and Supplementary Data 6-7).
Rare variants associated with T2D. Very few rare variantsassociated with T2D have been identified in previous studies [26][27][28] . We included 10,849,711 rare variants (0.0001 ≤ MAF < 0.01) in the association analysis in UKB and detected 11 rare variants at P < 5 × 10 −8 and 4 of them were at P < 5 × 10 −9 ( Fig. 1b and Supplementary Table 4). We focused only on the 4 signals at P < 5 × 10 −9 because a recent study suggested that a P value threshold of 5 × 10 −9 is required to control a GWFPR at 0.05 in GWAS, including both common and rare variants imputed from a fully sequenced reference 20 . Three of the rare variants were located at loci with significant common variant associations. Variant rs78408340 (odds ratio (OR) = 1.33, P = 4.4 × 10 −14 ) is a missense variant that encodes a p.Ser539Trp alteration in PAM and was reported to be associated with decreased insulin release from pancreatic beta cells 27 . Variant rs146886108 (OR = 0.72, P = 4.4 × 10 −9 ), which showed a protective effect against T2D, is a novel locus and a missense variant that encodes p.Arg187Gln in ANKH 29 . Variant rs117229942 (OR = 0.70, P = 4.0 × 10 −11 ) is an intron variant in TCF7L2 4 . Variant rs527320094 (OR = 2.74, P = 4.6 × 10 −9 ), located in LOC105378797, is also a novel rarevariant association, with no other significant SNP (either common or rare) within a ±1 Mb window. We did not observe any substantial difference in association signals for these 4 variants between the results from BOLT-LMM 30 and logistic regression 31 considering the difference in sample size (Supplementary Table 4).
Gene expression and DNA methylation associated with T2D. Most previous studies have reported the gene in closest physical proximity to the most significant SNP at a GWAS locus. However, gene regulation can be influenced by genetic variants that are physically distal to the genes 32 . To prioritize genes identified through the genome-wide significant loci that are functionally relevant to the disease, we performed a summary Columns are probe ID, probe chromosome, gene name, probe position, SNP name, SNP position, effect allele, other allele, frequency of the effect allele in the reference sample, GWAS P value, eQTL P value, SMR P value and HEIDI P value data-based Mendelian randomization (SMR) analysis 33 using the top-associated expression quantitative trait locus (eQTL) as an instrumental variable to test for association between the expression level of each gene and T2D (Methods). We used GWAS summary data from our meta-analysis and eQTL summary data from the eQTLGen (n = 14,115) and CAGE consortia (n = 2765) 34 for the SMR analysis (Methods). We identified 40 genes in eQTLGen and 24 genes in CAGE at an experimental-wise significance level (P SMR < 2.7 × 10 −6 , i.e., 0.05/m SMR , with m SMR ¼ 18; 602 being the total number of SMR tests in the 2 data sets) (Supplementary Data 8-9). To filter out the SMR associations due to linkage (i.e., 2 causal variants in LD, one affecting gene expression and the other affecting T2D risk), all the significant SMR associations were followed by a HEterogeneity In Dependent Instruments (HEIDI) 33 analysis to test whether there is heterogeneity in SMR estimates at SNPs in LD with the topassociated cis-eQTL (Methods). Therefore, genes not rejected by HEIDI (i.e., no evidence of heterogeneity) were those associated with T2D through pleiotropy at a shared genetic variant. Of the genes that passed the SMR test, 27 genes in eQTLGen and 15 genes in CAGE were not rejected by the HEIDI test (P HEIDI > 7.8 × 10 −4 , i.e., 0.05/m SMR , with m SMR ¼ 64 being the total number of SMR tests in the 2 data sets) (Tables 2-3 and Supplementary Data 8-9), with 7 genes in common and 33 unique genes in total. SNPs associated with the expression levels of genes including EHHADH (rs7431357), SSSCA1 (rs1194076), and P2RX4 (rs2071271) in eQTLGen were not significant in the T2D meta-analysis, likely due to the lack of power; these SNPs were expected to be detected in future studies with larger sample sizes.
To identify the regulatory elements associated with T2D risk, we performed SMR analysis using methylation quantitative trait locus (mQTL) data from McRae et al. 35 (n = 1980) to identify DNA methylation (DNAm) sites associated with T2D through pleiotropy at a shared genetic variant. In total, 235 DNAm sites were associated with T2D, with P SMR < 6.3 × 10 −7 m SMR ¼ 78; 961 ð Þand P HEIDI > 1.6 × 10 −4 m HEIDI ¼ 323 ð Þ(Supplementary Data 10); these DNAm sites were significantly enriched in promoters (fold change = 1.60, P enrichment = 1.6 × 10 −7 ) and weak enhancers (fold change = 1.74, P enrichment = 1.4 × 10 −2 ) (Supplementary Note 8 and Supplementary Fig. 9). Identification of DNAm sites and their target genes relies on consistent association signals across omics levels 11 . To demonstrate this, we conducted the SMR analysis to test for associations between the 235 T2D-associated DNAm sites and the 33 T2D-associated genes and identified 22 DNAm sites associated with 16  SMR associations in multiple T2D-relevant tissues. To replicate the SMR associations in a wider range of tissues relevant to T2D, we performed SMR analyses based on cis-eQTL data from 4 tissues in GTEx 36 (i.e., adipose subcutaneous tissue, adipose visceral omentum, liver, and pancreas). We denoted these 4 tissues as GTEx-AALP. Of the 27 putative T2D genes identified by SMR and HEIDI using the eQTLGen data, 10 had a cis-eQTL at P eQTL < 5 × 10 −8 in at least one of the 4 GTEx-AALP tissues (Supplementary Data 13). Note that the decrease in eQTL detection power is expected given the much smaller sample size of GTEx-AALP (n = 153-385) compared to that of eQTLGen (n = 14,115), as demonstrated by simulation (Supplementary Note 9 and Supplementary Fig. 10). As a benchmark, 17 of the 27 genes had a cis-eQTL at P eQTL < 5 × 10 −8 in GTEx-blood (n = 369). We first performed the SMR analysis in GTEx-blood and found that 12 of the 17 genes were replicated at P SMR < 2.9 × 10 −3 (i.e., 0.05/ 17) (Supplementary Data 13), an expected high replication rate given the simulation result ( Supplementary Fig. 10). We then conducted the SMR analysis in GTEx-AALP. The result showed that 8 of the 10 genes showed significant SMR associations at P SMR < 1.3 × 10 −3 (i.e., 0.05/40) in at least one of the 4 GTEx-AALP tissues, a replication rate comparable to that found in GTEx-blood. Among the 8 genes, CWF19L1, for which the cis-eQTL effects are highly consistent across different tissues, was significant in all the data sets ( Supplementary Fig. 11).
The replication analysis described above depends heavily on the sample sizes of eQTL studies. A less sample-size-dependent Columns are probe ID, probe chromosome, gene name, probe position, SNP name, SNP position, effect allele, other allele, frequency of the effect allele in the reference sample, GWAS P value, eQTL P value, SMR P value, and HEIDI P value approach is to quantify how well the effects of the top associated cis-eQTLs for all the 27 putative T2D genes estimated in blood (i.e., the eQTLGen data) correlate with those estimated in the GTEx tissues, accounting for sampling variation in estimated SNP effects 37 . This approach avoids the need to use a stringent P value threshold to select cis-eQTLs in the GTEx tissues with small sample sizes. We found that the mean correlation of cis-eQTL effects between eQTLGen blood and GTEx-AALP was 0.47 (s.e. = 0.16), comparable to and not significantly different from the value of 0.64 (s.e. = 0.16) between eQTLGen and GTExblood. We also found that the estimated SMR effects of 18 genes, which passed the SMR test and were not rejected by the HEIDI test in either eQTLGen or GTEx, were highly correlated (Pearson's correlation r = 0.80) (Supplementary Fig. 12). Note that this correlation is not expected to be unity because of differences in the technology used to measure gene expression (Illumina gene expression arrays for eQTLGen vs. RNA-seq for GTEx). We also performed co-localization analyses using COLOC 38 , a Bayesian approach to seek evidence of a locus associated with two traits. We found that most of the genes that passed the genome-wide significant threshold in the SMR test also had extremely high posterior probabilities of associations with T2D from the COLOC analysis ( Supplementary Fig. 13).
These results support the validity of using eQTL data from blood for the SMR and HEIDI analysis; using this method, we can make use of eQTL data from very large samples to increase the statistical power, consistent with the conclusions of a recent study 37 . In addition, tissue-specific effects that are not detected in blood will affect the power of the SMR and HEIDI analysis rather than generating false positive associations.
Putative regulatory mechanisms for 3 T2D genes. Here, we used the genes CAMK1D, TP53INP1, and ATP5G1 as examples to hypothesize possible mechanisms of how genetic variants affect T2D risk by controlling DNAm for gene regulation 11 . Functional gene annotation information was acquired from the Roadmap Epigenomics Mapping Consortium (REMC) 39 .
The significant SMR association of CAMK1D with T2D was identified in both eQTL data sets (Tables 2-3 and Supplementary Data 8-9). The top eQTL, rs11257655, located in the intergenic region (active enhancer) between CDC123 and CAMK1D, was also a genome-wide significant SNP in our meta-analysis (P = 2.0 × 10 −17 ). It was previously shown that rs11257655 is located in the binding motif for FOXA1/FOXA2 and that the T allele of this SNP is a risk allele that increases the expression level of CAMK1D through allelic-specific binding of FOXA1 and FOXA2 40 . Another functional study demonstrated that increasing the expression of FOXA1 and its subsequent binding to enhancers was associated with DNA demethylation 41 . Our analysis was consistent with previous studies in showing that the T allele of rs11257655 increases both CAMK1D transcription (β ¼ 0:553, s.e. = 0.014, where β is the allele substitution effect on gene expression in standard deviation units) and T2D risk (OR = 1.076, s.e. = 0.009) (Supplementary Data 8, 9, and 11). Moreover, rs11257655 was also the top mQTL (Fig. 2); the T allele of this SNP is associated with decreased methylation at the site cg03575602 in the promoter region of CAMK1D, suggesting that the T allele of rs11257655 up-regulates the transcription of CAMK1D by reducing the methylation level at cg03575602. Leveraging all the information above, we proposed the following model of the genetic mechanism at CAMK1D for T2D risk (Fig. 3). In the presence of the T allele at rs11257655, FOXA1/ FOXA2 and other transcription factors bind to the enhancer region and form a protein complex that leads to a decrease in the DNAm level of the promoter region of CAMK1D and recruits the RNA polymerase to the promoter, resulting in an increase in the expression of CAMK1D (Fig. 3). A recent study showed that the T risk allele is correlated with reduced DNAm and increased chromatin accessibility across multiple islet samples 42 and that it is associated with disrupted beta cell function 43 . Our inference highlights the role of promote-enhancer interaction in gene regulation, analytically indicated by the integrative analysis using the SMR and HEIDI approaches.
The second example is TP53INP1, the expression level of which was positively associated with T2D as indicated by the SMR analysis (Table 2 and Supplementary Data 8). This was supported by previous findings that the protein encoded by TP53INP1 regulated the TCF7L2-p53-p53INP1 pathway in such a way as to induce apoptosis and that the survival of pancreatic beta cells was associated with the level of expression of TP53INP1 44 . TP53INP1 was mapped as the target gene for three DNAm sites (cg13393036, cg09323728, and cg23172400) by SMR (Fig. 4). All 3 DNAm sites were located in the promoter region of TP53INP1 and had positive effects on the expression level of TP53INP1 and on T2D risk (Supplementary Data 8, 10, and 11). Based on these results, we proposed the following hypothesis for the regulatory mechanism (Fig. 5). When the DNAm level of the promoter region is low, expression of TP53INP1 is suppressed due to the binding of repressor(s) to the promoter. When the DNAm level of the promoter region is high, the binding of repressor(s) is disrupted, allowing the binding of transcription factors that recruit RNA polymerase and resulting in upregulation of gene expression. Increased expression of this gene has been shown to increase T2D risk by decreasing the survival rate of pancreatic beta cells through a TCF7L2-p53-p53INP1dependent pathway.
The third example involves 2 proximal genes, ATP5G1 and UBE2Z, the expression levels of which were significantly associated with T2D according to the SMR analysis (Table 2 and Supplementary Data 8). A methylation probe (cg16584676) located in the promoter region of UBE2Z was associated with the expression levels of both ATP5G1 and UBE2Z (Supplementary Fig. 14a), suggesting that these two genes are co-regulated by a genetic variant through DNAm. The effect of cg16584676 on gene expression was negative (Supplementary Data 11 and 12), implying the following plausible mechanism. A genetic variant near ATP5G1 exerts an effect on T2D by increasing the DNAm levels of the promoters for ATP5G1 and UBE2Z; this decreases the binding affinity of the transcription factors that recruit RNA polymerase, resulting in down-regulation of gene expression and ultimately leading to an increase in T2D risk ( Supplementary  Fig. 14b). ATP5G1 has been shown to encode a subunit of mitochondrial ATP synthase, and UBE2Z is a ubiquitinconjugating enzyme. Insulin receptors could be degraded by SOCS proteins during ubiquitin-proteasomal degradation, and ATP5G1 and UBE2Z are likely to be involved in this pathway 45 . The function of insulin receptors is to regulate glucose homeostasis through the action of insulin and other tyrosine kinases, and dysfunction of these receptors leads to insulin resistance and increases T2D risk.
The 3 examples above provide hypotheses for how genetic variants may affect T2D risk through regulatory pathways and demonstrate the power of integrative analysis of omics data for this purpose. These examples describe putative candidates that could be prioritized in future functional studies.
Potential drug targets. In the SMR analysis described above, we identified 33 putative T2D genes. We matched these genes in the DrugBank database (see URLs section) and found that 3 genes (ARG1, LTA, and P2RX4) are the targets of several approved drugs (drugs that have been approved in at least one jurisdiction). ARG1 (UniProt ID: P05089), whose expression level was negatively associated with T2D risk, is targeted by three approved drugs: ornithine (DrugBank ID: DB00129), urea (DrugBank ID: DB03904), and manganese (DrugBank ID: DB06757), but the pharmacological mechanism of action of these drugs remains unknown. Arginase (ARG1 is an isoform of arginase in liver) is a manganese-containing enzyme that catalyzes the hydrolysis of arginine to ornithine and urea. Arginase in vascular tissue might be a potential therapeutic target for the treatment of vascular dysfunction in diabetes 46 . Metformin, an oral antidiabetic drug that is used in the treatment of diabetes, was reported to increase ARG1 expression in a murine macrophage cell line 47 , consistent with our SMR result that increased expression of ARG1 was associated with decreased T2D risk (Supplementary Data 8). There was also evidence for an interaction between ARG1 and metformin (Comparative Toxicogenomics Database, see URLs section). The likely mechanism is that metformin activates AMPactivated protein kinase (AMPK), resulting in increased expression of ARG1 48 , again consistent with our SMR result. LTA (UniProt ID: P08637), whose expression level was negatively associated with T2D risk, is targeted by the approved drug etanercept (DrugBank ID: DB00005) for rheumatoid arthritis (RA) treatment. P2RX4 (UniProt ID: Q99571), the expression level of which was positively associated with T2D risk, is targeted by eslicarbazepine acetate (DrugBank ID: DB09119; antagonist for P2RX4). Eslicarbazepine acetate is an anticonvulsant that inhibits repeated neuronal firing and stabilizes the inactivated state of voltage-gated sodium channels; its pharmacological action makes it useful as an adjunctive therapy for partial-onset seizures 49 . Antagonists of P2RX4 inhibit high glucose and are useful in the treatment of diabetic nephropathy 50 . We also explored whether any of these three genes have potential adverse effects by checking the associations of the lead variants at the three loci with lipid-    Table 5). Under an evolutionary neutral model and a constant population size 52 , the explained variance is uniformly distributed as a function of MAF, which means that the variance explained by variants with MAF ≤ 0.1 equals that explained by variants with MAF > 0.4. However, in our results, the MAF bin containing low-MAF and rare variants (MAF ≤ 0.1) showed a larger estimate than any other MAF bin (Fig. 6a and Supplementary Table 5), consistent with a model of negative (purifying) selection or population expansion 53 . To further distinguish between the two models (negative selection vs. population expansion), we performed an additional analysis using a recently developed method, BayesS 54 (implemented in GCTB, see URLs section) to estimate the relationship between variance in effect size and MAF (Methods). The method also allowed us to estimatê h 2 SNP and polygenicity (π) on each chromosome. The results (Fig. 6b) showed that theĥ 2 SNP of each chromosome was highly correlated with its length (Pearson's correlation r = 0.92). The mean estimate of π, i.e., the proportion of SNPs with non-zero effects, was 1.75% across all chromosomes (Fig. 6c and Supplementary Table 6), suggesting a high degree of polygenicity for T2D. The sum of per-chromosomeĥ 2 SNP from BayesS was 31.9% (s.e. = 4.1%) on the liability scale, slightly higher than that based on HapMap3 SNPs from a Haseman-Elston regression analysis (28.7%, s.e. = 1.1%) using a full set of unrelated UKB individuals (n = 348,580) or from an LD score regression analysis (22.6%, s.e. = 1.2%) using all the UKB individuals (n = 455,607) (Supplementary Table 7). The variance in effect size was significantly negatively correlated with MAF (Ŝ = −0.53, s.e. = 0.09), consistent with a model of negative selection on deleterious rare alleles (Fig. 6d) and inconsistent with a recent study 9 concluding that T2D-associated loci have not been under natural selection. Our conclusion regarding negative selection is also consistent with the observation that the minor alleles of 9 of the 11 rare variants at P<5 10 À8 were T2D risk alleles (Supplementary Table 4). The signal of negative selection implies that a large number of rare variants are expected to be discovered in future GWAS in which appropriate genotyping strategies are used.

Discussion
In this study, we sought to identify novel genetic loci associated with T2D by a meta-analysis of GWAS with a very large sample size and to infer plausible genetic regulation mechanisms at known and novel loci by an integrative analysis of GWAS and omics data. We identified 139 near-independent common variants P<5 10 À8 ð Þand 4 rare variants P<5 10 À9 ð Þfor T2D in the meta-analysis. Of the 139 common loci, 39 were novel compared with the results of all 49 previous T2D GWAS from the GWAS Catalog (see URLs section) 55 , including the 2 recent studies by DIAGRAM 56 and Zhao et al. 57 . We did not detect evidence for sex or age heterogeneity in UKB (Supplementary Gene (CAMK1D) Fig. 3 Hypothesized regulatory mechanism at the CAMK1D locus for T2D. When the allele of rs11257655 in the enhancer region (red) changes from C to T, the enhancer activator protein FOXA1/FOXA2 (orange ellipsoid) binds to the enhancer region and the DNA methylation level in the promoter region is reduced; this increases the binding efficiency of RNA polymerase II recruited by mediator proteins (gray circles) and, therefore increases the transcription of CAMK1D Note 11, Supplementary Fig. 14, and Supplementary Table 8). By integrating omics data, we have inferred the genetic mechanisms for the 3 genes CAMK1D, TP53INP1, and ATP5G1; the inferred mechanisms suggest that enhancer-promoter interactions with DNA methylation play an important role in mediating the effects of genetic variants on T2D risk. These findings provide deeper insight into the etiology of T2D and suggest candidate genes for functional studies in the future. Furthermore, our estimation of genetic architecture suggests that T2D is a polygenic trait for which both rare and common variants contribute to the genetic variation and indicates that rarer variants tend to have larger effects on T2D risk ( Fig. 6c and Supplementary Table 4). Assuming that most new mutations are deleterious for fitness, our result is consistent with a model in which mutations that have larger effects on T2D (and thereby on fitness through pleiotropy) are more likely to be maintained at low frequencies in the population by negative (purifying) selection.   This study has a number of limitations. First, the SNP-T2D associations identified by the meta-analysis might be biased by misdiagnosis of T1D (type 1 diabetes) and latent autoimmune diabetes in adults 58 . Previous studies found that biases in SNP-T2D associations due to misdiagnosis are likely to be very modest 5,56 . We showed by 2 additional analyses based on known T1D loci that most of the novel SNP-T2D associations identified in this study are unlikely to be driven by misdiagnosed T1D cases (Supplementary Note 12 and Supplementary Data 15). Second, some of the T2D-associated SNPs might confer T2D risk through mediators such as obesity or dyslipidemia. To explore this possibility, we performed a summary data-based conditional analysis of the 139 T2D-associated SNPs conditioning on body mass index (BMI) or dyslipidemia by GCTA-mtCOJO 59 using GWAS data for these 2 traits from UKB. It appeared that the effect sizes of most T2D-associated SNPs, with the exception of a few outliers (e.g., FTO, MC4R, POCS, and TFAP2B), were not affected by BMI or dyslipidemia (Supplementary Fig. 16). These outliers were among those showing the strongest associations with BMI 60 . Third, among the 39 novel loci, there was only 1 locus (ARG1/ MED23, Supplementary Fig. 17) at which the association between gene expression and T2D risk was significant in SMR and not rejected by HEIDI (Tables 2-3). This is because the power of the SMR test depends primarily on the SNP effect from GWAS 10 , which is small for the novel loci. Fourth, the sample sizes of eQTL data from the disease relevant tissues were relatively small. We used the eQTL data from blood to take advantage of the large sample sizes. This maximized the power for detecting genes for which the eQTL effects are consistent across tissues (Supplementary Fig. 10) but might have missed genes for which the eQTL effects are specific to the T2D-relevant tissues. Moreover, the pancreatic islets constitute only 1-2% of the whole pancreas volume 61 and previous studies revealed islet-specific gene activity for T2D 62,63 . Therefore, in our SMR analysis using GTEx-pancreas data, genes with islet-specific transcription or eQTL effects could be missed. Finally, we employed the SMR and HEIDI methods to map CpG sites to their target genes and to identify the CpG sites associated with T2D because of pleiotropy. The SMR approach uses genome-wide significant mQTL as an instrumental variable for each CpG site, which requires a large sample size for the mQTL discovery. In this study, we used mQTL data based on Illumina HumanMethylation450 arrays because of the relatively large sample size (n = 1980). Unfortunately, we did not have access to mQTL data from whole-genome bisulfite sequencing (WGBS) in a large sample. Nevertheless, it is noteworthy that there are three T2D-associated variants at the CAMK1D/CDC123, ADCY5, and KLHDC5 loci that show hypomethylation and allelic imbalance as identified by Thurner et al. 42 using WGBS data (n = 10), all of which were genome-wide significant in our mQTL-based SMR analysis. In addition, a previous study showed that T2D-associated loci were enriched in islet stretch enhancers 63 ,~54.1% of which were tagged by at least one of the DNAm probe in the 450 K array (annotation data from ref. 64 ). Despite these limitations, our study highlights the benefits of integrating multiple omics data to identify functional genes and putative regulatory mechanisms driven by local genetic variation. Future applications of integrative omics data analyses are expected to improve our understanding of the biological mechanisms underlying T2D and other common diseases.

Methods
Summary statistics of DIAGRAM, GERA, and UKB. The data used in this study were derived from 659,316 individuals of European ancestry and a small cohort from Pakistan, and were obtained from three data sets: DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) 5 , Genetic Epidemiology Research on Adult Health and Aging (GERA) 12 5 Hypothesized regulatory mechanism at the TP53INP1 locus for T2D. When the promoter region is highly methylated, which prevents binding of repressor protein (red rounded rectangle) to the promoter region, RNA polymerase II (green ellipsoid), transcription factor protein (orange ellipsoid) and mediator proteins (gray circles) will form a transcription initiation complex that increases the transcription. However, when the methylation level of the promoter region is low, repressor protein can more efficiently bind to the promoter, blocking the binding of the transcription initiation complex to the promoter, which decreases the transcription of TP53INP1 descent, and the genotype data were imputed to the HapMap2 Project 65 (~2.5 million SNPs after quality control). In stage 2, there were 22,669 cases and 58,119 controls genotyped on Metabochips (~137,900 SNPs), including 1178 cases and 2472 controls of Pakistani descent. There was limited evidence of genetic heterogeneity between individuals of European and those of Pakistani descent for T2D 5 . The sample prevalence was 23.3% (17.6% in stage 1 and 28.1% in stage 2). We imputed the stage 1 summary statistics by ImpG 15 and combined the imputed data with stage 2 summary statistics (Supplementary Note 1). GERA: There were 6905 cases and 46,983 controls in GERA, and the sample prevalence was 12.4%. We cleaned the GERA genotype data using standard quality control (QC) filters (excluding SNPs with missing rate ≥ 0.02, Hardy-Weinberg equilibrium test P value ≤ 1 × 10 -6 or minor allele count ≤ 1 and removing individuals with missing rate ≥ 0.02) and imputed the genotype data to the 1000 Genomes Projects (1KGP) reference panels 14 using IMPUTE2 66 . We used GCTA 67 (see URLs section) to compute the genetic relationship matrix (GRM) of all the individuals based on a subset of imputed SNPs (HapMap3 SNPs with MAF ≥ 0.01 and imputation info score ≥ 0.3), removed the related individuals at a genetic relatedness threshold of 0.05, and retained 53,888 individuals (6905 cases and 46,983 controls) for further analysis. We computed the first 20 principal components (PCs) from the GRM. The summary statistics in GERA were obtained from a GWAS analysis using PLINK2 31 with sex, age, and the first 20 PCs fitted as covariates. To examine the influence of imputation panel on the meta-analysis result, we further imputed GERA to the HRC 68 using the Sanger imputation service (see URLs section).
UKB: Genotype data from UKB were cleaned and imputed to HRC by the UKB team 13 . There were 21,147 cases and 434,460 controls, and the sample prevalence was 5.5%. We identified a European subset of UKB participants (n = 456,426) by projecting the UKB participants onto the 1KGP PCs. Genotype probabilities were converted to hard-call genotypes using PLINK2 31 (hard-call 0.1), and we excluded SNPs with minor allele count < 5, Hardy-Weinberg equilibrium test P value < 1 × 10 -6 , missing genotype rate > 0.05, or imputation info score < 0.3.
The UKB phenotype was acquired from self-report, ICD10 main diagnoses and ICD10 secondary diagnoses (field IDs: 20002, 41202, and 41204). The GWAS analysis in UKB was conducted in BOLT-LMM 30 with sex and age fitted as covariates. In the BOLT-LMM analysis, we used 711,933 SNPs acquired by LD pruning (r 2 < 0.9) from Hapmap3 SNPs to control for relatedness, population stratification and polygenic effects. We transformed the effect size from BOLT-LMM on the observed 0-1 scale to the OR using LMOR 69 .
Inverse variance based meta-analysis. Before conducting the meta-analysis, we performed several analyses in which we examined genetic heterogeneity and sample overlap among data sets (Supplementary Note 2). We performed a 2-stage meta-analysis. The first stage combined DIAGRAM stage 1 (GWAS chip) data with GERA and UKB. The second stage combined DIAGRAM stage 1 and 2 (GWAS chip and metabolism chip) with GERA and UKB. We extracted the SNPs common to the 3 data sets (5,526,193 SNPs in stage 1 and 5,053,015 million SNPs in stage 2) and performed the meta-analyses using an inverse-variance based method in METAL 16 . The stage 2 meta-analysis data were used in the follow-up analyses.
Summary-data-based Mendelian randomization analysis. We performed SMR and HEIDI analyses 10 to identify genes whose expression levels were associated with a trait due to pleiotropy using summary statistics from GWAS and eQTL/ mQTL studies. We first performed the SMR analysis to test for association between the expression level of each gene and the disease using the top associated cis-eQTL of the gene as an instrumental variable (in a Mendelian randomization analysis framework). There are at least two models consistent with an observed SMR association, i.e., pleiotropy (a genetic variant having effects on both trait and gene expression) and linkage (2 genetic variants in LD, one affecting the trait and another affecting gene expression). The HEIDI test 10 uses multiple SNPs in a cis-eQTL region to distinguish pleiotropy from linkage by testing whether there is heterogeneity in SMR effects estimated at different SNPs in LD with the top associated cis-eQTL. We used the SMR and HEIDI methods to test for pleiotropic associations between gene expression and T2D, between DNAm and T2D, and between T2D-associated gene expression and T2D-associted DNAm. In the SMR analysis, we used eQTL summary data from the eQTLGen Consortium (n = 14,115 in whole blood), the CAGE (n = 2765 in peripheral blood) 34 and the GTEx v7 release (n = 385 in adipose subcutaneous tissue, n = 313 in adipose visceral omentum, n = 153 in liver, n = 220 in pancreas and n = 369 from whole blood) 36 . In CAGE and eQTLGen, gene expression levels were measured using Illumina gene expression arrays; in GTEx, gene expression levels were measured by RNA-seq. The SNP genotypes in all cohorts were imputed to 1KGP. The cis-eQTL within 2 Mb of the gene expression probes with P eQTL < 5 × 10 −8 were selected as the instrumental variables in the SMR test. The mQTL summary data were obtained from genetic analyses of DNA methylation measured on Illumina HumanMethy-lation450 arrays (n = 1980 in peripheral blood) 35 . We used mQTL data generated by the 450 K methylation arrays rather than whole-genome bisulfite sequencing (WGBS) because WGBS-based mQTL data of large sample size (at least 100 s) are not available yet. We demonstrated the statistical power of SMR test in our study by simulation under a pleiotropy model (Supplementary Note 9 and Supplementary Fig. 10).
Estimating the genetic architecture for T2D. The MAF-and LD-stratified GREML (GREML-LDMS) is a method for estimating SNP-based heritability that is robust to model misspecification 51,70 . For ease of computation, we limited the analysis to a subset of unrelated UKB individuals (15,767 cases and 104,233 controls); in this subset, we kept all 15,767 cases among the unrelated individuals to maximize the sample size of cases and randomly selected 104,233 individuals from 332,813 unrelated controls. We first estimated the segment-based LD score, stra-tified~18 million SNPs into 2 groups based on the segment-based LD scores (high vs. low LD groups separated by the median), and then stratified the SNPs in each LD group into 7 MAF bins (10 −4 to 10 −3 , 10 −3 to 10 −2 , 10 −2 to 10 −1 , 0.1-0.2, 0.2-0.3, 0.3-0.4, and 0.4-0.5). We computed the GRMs using the stratified SNPs and performed GREML analysis fitting 14 GRMs (with sex, age, and the first 10 PCs fitted as covariates) in one model to estimate the SNP-based heritability in each MAF bin. We used 10% as the population prevalence to convert the estimate to that on the liability scale.
We used GCTB-BayesS 54 to estimate the joint distribution of SNP effect size and allele frequency. This analysis is based on 348,580 unrelated individuals (15,767 cases and 332,813 controls) and HapMap3 SNPs (~1.23 million) with sex, age, and the first 10 PCs fitted as covariates. Each SNP effect has a mixture prior of a normal distribution and a point mass at zero, with an unknown mixing probability, π, representing the degree of polygenicity. The variance in effect size is modeled to be dependent on MAF through a parameter S. Under an evolutionarily neutral model, SNP effect sizes are independent of MAF, i.e., S = 0. A negative (positive) value of S indicates that variants with lower MAF are prone to having larger (smaller) effects, consistent with a model of negative (positive) selection. A Markov-chain Monte Carlo (MCMC) algorithm was used to draw posterior samples for statistical inference. The posterior mean was used as the point estimate, and the posterior standard error was approximated by the standard deviation of the MCMC samples. We conducted the analysis chromosome-wise for ease of computation.