Population-specific methods were applied to calculate single nucleotide polymorphism-based heritability within each ancestry. Statistically significant single nucleotide polymorphism-based heritability for CanUD was observed in all but the smallest population (East Asian). We discovered genome-wide significant loci unique to each ancestry: 22 in European, 2 each in African and East Asian, and 1 in admixed American ancestries. A genetically informed causal relationship analysis indicated a possible effect of genetic liability for CanUD on lung cancer risk, suggesting potential unanticipated future medical and psychiatric public health consequences that require further study to disentangle from other known risk factors such as cigarette smoking.As recreational use of cannabis is being decriminalized in many places and medical use widely sanctioned, there are growing concerns about increases in cannabis use disorder (CanUD), which is associated with numerous medical comorbidities. Here we performed a genome-wide association study of CanUD in the Million Veteran Program (MVP), followed by meta-analysis in 1,054,365 individuals ( Multi-ancestry genome-wide association meta-analyses identify risk loci for cannabis use disorder. Genomic structural equation modeling and genetic correlation analyses show overlap with several other traits, including impulsivity and psychopathology. Substantial negative health outcomes associated with chronic cannabis use include various cancers associated with inhaling combustion products3, declines in cognitive capacity and motivation and increased schizophrenia (SCZ) risk5. Individual and societal complications that result from CanUD include decreased productivity and accidents related to intoxication6. The full range of risks and negative outcomes associated with cannabis use and CanUD may not be appreciated widely. Considering the gradually increasing permissiveness surrounding its use, understanding various sources of risk that influence CanUD is both necessary and timely.Cannabis is a psychoactive substance with a long history of use and dependence. Recently within the United States, 37 states have approved what is termed medical cannabis use, and 19 states, 2 territories and the District of Columbia allow possession of cannabis for recreational purposes. In Europe, only Malta has fully legalized recreational cannabis, although many other countries have decriminalized possession of small amounts of cannabis and have enabled medical allowances. It was recently legalized in Thailand but remains prohibited in many parts of Asia, the Middle East and South America. The status in many of these places may be subject to change in the near future. More than a third of individuals who use cannabis develop cannabis use disorders (CanUD), and evidence regarding the impact of legalization on escalating use and use disorders is mixed8 and Mass General Brigham (MGB) BioBank9 and meta-analyzed these with the Psychiatric Genomics Consortium (PGC)/deCODE/iPSYCH1 study10. MVP, one of the largest biobanks in the world11, has enabled a substantial increase in power for genomic discovery by doubling the number of cases of European (EUR) ancestry available. By increasing sample numbers, we substantially increased the number of discovered loci and confirmed previous findings10. We also leveraged the ancestral diversity of the MVP to expand analyses of African ancestry individuals (AFR) and conducted genome-wide association studies (GWAS) analyses in Admixed American (AMR) and East Asian (EAS) ancestries. Linkage disequilibrium (LD) score regression (LDSC) can quantify variance explained by genetics and identify overlap between traits. This method is sufficient for EUR ancestries but not appropriate for some non-European and admixed ancestries. To solve this problem, we used cohort-derived covariate LDSC12 to calculate single nucleotide polymorphism (SNP)-based heritability in these populations, finding similar results among all ancestries. We conducted a transcriptome-wide association study (TWAS), which leverages annotations based on variant associations to changes in gene expression, in adult and fetal brain tissue to identify significant expression quantitative trait loci (eQTLs), using stratified LDSC to show enriched SNP-based heritability in fetal but not adult cortex. We also conducted Mendelian randomization (MR) analyses—an approach that uses genetic variations identified by GWAS as instruments to obtain an unbiased estimate of the effect of a trait of interest  on outcomes—to examine causal relationships with chronic pain, lung cancer, physical activity and SCZ. Finally, we performed genomic structural equation modeling (gSEM)—a multivariate method for analyzing GWAS summary statistics to examine joint genetic architecture of traits—to understand the genomic relationships between cannabis use traits and other psychiatric and substance use disorder (SUD) traits. This work builds upon a decade of progress in the field18.In this Article, we combined genome-wide genotype data from the Million Veteran Program (MVP) with expanded samples from iPSYCH2CHRNA2 , which encodes cholinergic receptor nicotinic alpha 2 subunit, consistent with prior GWAS10; the lead SNP was identical to one prior study7. Findings for AFR include a SNP in an intron of SLC36A2 , which encodes a pH-dependent proton-coupled amino acid transporter for glycine, alanine and proline. The lead SNP in AMR was rs9815757 (P = 4.4 × 10−8). The lead SNP in EAS  is intronic to SEMA6D, which encodes semaphorin 6D , rs7029483 (130 kb upstream of MTND2P8), rs2627197 (intronic to ENO4), rs34438449 (40 kb downstream of MIR5007) and rs147144681 (intronic to CHRNA3).We assembled a total sample of 886,025 EUR participants across five datasets  = 0.017), AFR h2 = 8.1% (s.e. = 0.013), and AMR h2 = 18.0% (s.e. = 0.042). There was high variance and a high point estimate in AMR. LDSC was used to calculate genetic correlation between cannabis use dependence cohorts included in this meta-analysis and also within MVP phenotype definitions  included in the meta-analysis yielded high genetic correlation, with 19 for CanUD in African ancestry and a selection of traits represented in Fig. Genetic correlations were calculated against available traits using POPCORNβ = 0.46, P = 2.90 × 10−5). There was a bidirectional causal effect of CanUD and SCZ . CanUD showed a unidirectional effect on lung cancer   20. Two different datasets were used: smoking initiation and cigarettes per day. Individual runs were performed for the two cigarette smoking traits. A proportion of 18 of 22 original lead SNPs remained in the dataset following conditioning on smoking initiation (meaning they matched with variants in the conditioning data). For two out of four remaining SNPs, there were proxy SNPs in LD with each lead SNP showing GWS P values. Only rs545943750 and rs184064410 were excluded after conditioning due to missingness in the smoking data, leaving 20 of 22 lead loci from the CanUD GWAS available in the conditional analysis. All 20 remained GWS following conditioning. The results were similar with CanUD conditioning on cigarettes per day, with the same 20 lead loci remaining GWS after conditioning. Conditional analysis with smoking initiation or cigarettes per day did not substantially alter the magnitude of the lead CHRNA2 association (Pcond = 2.14 × 10-14). We used these summary statistics conditioned on cigarette smoking initiation to re-test the causal relationship between CanUD and lung cancer, and while the signal attenuated, it was still significant . The conditional analysis with cigarettes per day, however, removed the effect of CanUD on lung cancer (P = 0.79).For EUR, we performed a multi-trait conditional and joint analysis (mtCOJO) of CanUD conditioned on two smoking traits from the GWAS and Sequencing Consortium of Alcohol and Nicotine use study to investigate potential confounding effectsP < 5 × 10−8 for CanUD  and the Fagerström Test for Nicotine Dependence (FTND), we conducted an multi-trait analysis of GWAS (MTAG) analysis that identified 34 lead SNPs at 26 genomic risk loci, including four novel loci compared to the EUR meta-analysis, at P < 2.5 × 10−6) using adult and fetal brain frontal cortex expression, respectively, with six genes in common  , 5q12.1 , 11q23.2 (adult: RP11-629G13.1) and 16q22.2 (adult: PHLPP2). Protein functions of these genes are described in the Discussion below. The remaining set of genes identifies 38 candidate novel genetic loci associated with CanUD, with potential underlying transcriptomic mechanisms in either adult or fetal brain cortex  Fig. . The obsρ = 0.54, P < 2.2 × 10−16; Fig. Standardized TWAS effect sizes estimated using adult and fetal brain frontal cortex expression models showed moderate correlation , a four-factor model fit the data best, with the cumulative variance explained being 0.789, distributed relatively evenly across the four factors, with each accounting for between 22.7% and 29.2% of the overall variance explained . Each of the four factors had high sums of square (SS) loadings .r = 0.65), factors 1 and 3 (r = 0.64), factors 1 and 4 (r = 0.52) and factors 3 and 4 (r = 0.53). All correlations and loadings are summarized in Fig. Using confirmatory factor analysis (CFA) to evaluate the four-factor model that allowed all factors to intercorrelate had a comparative fit index of 0.913, a standardized root mean square residual of 0.068, a chi-squared value of 1397.5 and an Akaike information criterion of 1483.5. Traits loading most strongly on factor 1 included ‘Unable to work’ (loading of 1.06 ± 0.04), Townsend deprivation index (loading of 0.56 ± 0.03), chronic pain (loading of 0.50 ± 0.04) and FTND (loading of 0.45 ± 0.07). Traits loading most strongly on factor 2 included number of sex partners (loading of 0.91 ± 0.02), cannabis use (loading of 0.70 ± 0.03) and initiation of regular smoking (loading of 0.58 ± 0.03). Psychiatric traits loaded most strongly on factor 3 and included major depressive disorder (MDD) (loading of 0.95 ± 0.02), post-traumatic stress disorder (PTSD) checklist score (PCL) total (loading of 0.88 ± 0.04), generalized anxiety disorder symptoms (loading of 0.86 ± 0.03), suicide attempt (loading of 0.59 ± 0.05) and SCZ (loading of 0.29 ± 0.02). SUD traits loaded most strongly on factor 4 and included CanUD (loading of 0.96 ± 0.03), opioid use disorder (loading of 0.85 ± 0.05) and AUD (loading of 0.81 ± 0.03). There were moderate correlations between factors 2 and 4  and FOXP2 , with triple the effective sample size of the largest of those studies10, demonstrating once again the stability of GWAS findings as sufficient sample size and power to discover new loci are reached23. We discovered GWS loci in four ancestral groups: EUR, AFR, AMR and EAS. In AFR, two independent SNPs were associated on chromosome 5. The first (rs574008891) was within an intron of the gene that encodes methylcrotonyl-CoA carboxylase subunit 2 (MCCC2). The other significant locus (rs573117193) mapped to an intron in the solute carrier family 36 member 2 (SLC36A2) gene. These specific variants are absent in the other ancestries studied. For AMR, the one risk locus was rare  0.1%) and mapped in an intergenic region downstream of leucine rich repeat containing 3B (LRRC3B). Finally, for EAS, one locus was associated with CanUD: rs78561048, near semaphorin 6D (SEMA6D). Follow-up analysis in larger samples is needed to assess the robustness of findings, particularly in AMR and EAS. Several variants showed concordant direction of effect across all four stratified ancestral groups (Table P < 0.05) with same effect direction in AFR (0.04) and AMR (0.03) and significant in the multi-ancestry meta-analysis. This intronic variant of the protein phosphatase 6 catalytic subunit (PPP6C) is an eQTL for PPP6C, a gene linked to various cancers, including skin melanoma and lung squamous cell carcinoma. Multi-ancestry meta-analysis revealed an additional five loci not identified in the stratified analyses. Among them, the lead SNP on chromosome 15, rs147144681, which maps to an intron of the cholinergic receptor nicotinic alpha 3 subunit (CHRNA3) gene, is particularly noteworthy; as reported above, variation in CHRNA2 was among the first variants associated with CanUD and was replicated here. This suggests potential convergence involving the cholinergic system broadly and nicotinic receptors, specifically in the underlying etiology of CanUD. While nicotinic receptors are also associated with tobacco smoking-related traits24, the relative pattern of association for those traits is different from the observations for CanUD—for many smoking-related traits, a chromosome 15 nicotinic receptor cluster is associated with orders of magnitude greater support than other variants, including other nicotinic receptors; for CanUD, CHRNA2 is consistently the strongest association, also by orders of magnitude. We conducted conditional analysis for CHRNA2 and found the conditional P value remained robust following conditioning on smoking initiation20 (Pcond = 4.6 × 10−14). This replicates similar analyses performed by Demontis et al.7 and Johnson et al.10, which showed conditioning on smoking did not affect the CanUD association at this variant. Several other loci near cholinergic receptor subunit genes previously identified for smoking are not significant in our analysis of CanUD . Conversely, the CHRNA3 variant we find associated with CanUD is not significant for smoking  (ref. 20).We identified 22 significant loci, most of them novel, for CanUD in EUR. We also replicated findings in rG were tested for causal inference based on a combination of significant genetic correlation and a prior interest in phenotype . We identified a bidirectional causal relationship between CanUD and SCZ. At the same time, the MR Egger analysis indicated this was not due to horizontal pleiotropy. This supports similar findings reported previously, confirming previous genetic–epidemiologic studies25 and verifying an important public health risk associated with CanUD. To highlight differences between cannabis use and CanUD, we compared the pattern of genetic correlations across 18 traits, which showed striking differences. CanUD was much more closely associated with psychopathology, recapitulating a general pattern seen with other comparisons of SUD and use traits26. For example, while we observed a substantial negative correlation between CanUD and educational attainment, cannabis use was associated with greater educational attainment. POPCORN was used to generate a cross-covariance score to allow for comparison of traits across ancestries using genetic correlations for EUR and AFR groups  also become a significant factor29. Our MR results suggesting that chronic pain has a causal influence on CanUD emphasize the need for follow-up investigations that address whether greater consideration should be given to the adverse effects, rather than just the therapeutic effects among individuals receiving cannabis-based medicines. A similar question arises with opioids, which although often prescribed for pain, can also cause great harm30: namely, what level of risk of CanUD is acceptable given cannabis’ potential to improve quality of life and reduce opioid exposure in chronic pain patients? Our results suggest that harms such as dependence and consequences, reflected in underlying genetics of the trait, may need to be weighed against the potential benefits of cannabis treatment for chronic pain. Future studies should consider this novel relationship to pain31 and clinical efficacy trials are underway.Chronic pain may be a factor driving CanUD in some individuals, with significant unidirectional evidence for a causal effect of chronic pain32. The influence of cannabis on cancer risk is less well understood; it should be anticipated that these combustion products could have harmful pulmonary impacts—indeed, it would be surprising if smoking tobacco, but not smoking cannabis, increased cancer risk. MR yielded evidence for a unidirectional causal effect of CanUD on lung cancer. This result was robust to conditioning on data from the largest available smoking initiation GWAS but not conditioning on cigarettes per day, both traits that also have causal relationships with lung cancer but far more robust genetic instruments to evaluate this relationship. We do not currently have a way to assess genetic variation associated with the route of cannabis administration, but combustion is by far the most common method in the MVP and other cohorts studied. Given the trend toward increased legalization and usage, this apparent causal association needs to be monitored as it may have profound and underappreciated public health consequences. As the causal relationship with CanUD was not robust to conditioning on cigarettes per day, one probable explanation may be that there is horizontal pleiotropy between these traits in their influence on lung cancer.Cigarette smoking substantially increases the risk of many forms of cancer, including lung cancer, through numerous well-studied mechanisms with established literature dating back more than 60 years33 and fetal34 cortical tissue. These were DALRD3 , ERCC8 , RP11-629G13.1 (adult) and PHLPP2 (adult). The DALRD3 protein product, a DALR anticodon binding domain, forms a complex with the product of METTL2B. Nonsense mutations in DALRD3 are associated with developmental delay and early-onset epileptic encephalopathy35. ERCC8 encodes the excision repair 8, CSA ubiquitin complex subunit, which plays a role in DNA repair and is associated with the developmental disorder Cockayne syndrome36, as well as breast, esophageal and other cancers38. RP11-629G13.1 is a long noncoding RNA associated with downregulation of NCAM1 gene expression in multiple myeloma patients39. Significant partitioned SNP-based heritability was observed in fetal but not in the adult cortex, with 4.36% of trait SNP-based heritability explained by 0.12% of the total SNPs near fetal frontal cortex eQTLs. Only 1.77% of CanUD SNP-based heritability was explained using 0.13% of the total SNPs near adult cortex eQTLs. Fetal development may play a role in SUD susceptibility40, and substance use can influence fetal development during pregnancy and health outcomes during childhood41. Although exogenous exposure to cannabis may not occur until years or decades after birth, enriched fetal SNP-based heritability in this study argues a possible role for genetic effects on CanUD in the developing brain independent of exposure. SCZ risk is also modulated by risk factors during fetal development42 and genetic43 and environmental effects . Temporal convergence of the initiation of genetic risk effects for both SCZ and CanUD, if validated experimentally, would provide insight into the genetic relationship between these disorders and could relate to a mechanism for the bidirectional risk relationship between cannabis use and SCZ.Four GWS loci overlapped with TWAS prioritization from the EUR meta-analysis, using eQTL integration from samples of adult45.gSEM was used to contextualize summary statistics from this project with those from other published GWAS studies. Exploratory and confirmatory factor analyses showed that four factors provide the best fit for the 14 correlated traits included in the analysis. Factors fit mostly into categories that relate to functional impairment (factor 1), impulsivity and risk taking (factor 2), psychopathology (factor 3) and substance dependence (factor 4). CanUD fit best (and strongly) in the substance dependence cluster (factor 4). FTND fit into factors for functional impairment and substance dependence. Suicide attempts fit into functional impairment, impulsivity/risk taking and psychopathology. This is consistent with research showing overlapping pathologies within addiction and shared genetic risk factors between themThis study has limitations. The use of electronic health records allows for a large sample of CanUD cases but limits the assessment of subdiagnostic cannabis use in controls. Although we accounted for subdiagnostic cannabis users by excluding them from controls when information was available, these are probably underreported. Future studies of individuals with ascertained cannabis use who do not meet criteria for CanUD would provide more insight into the specific genetic liability to dependence. As the traits of interest were gathered from previously published reports or queries of electronic health records (EHRs) for diagnostic codes, we did not have information regarding tetrahydrocannabinol (THC) blood levels or information on the potency of cannabis at each exposure. If these data were available, study of effects on cannabis potency on dependence and comorbidities would be of great interest. We identified a causal relationship between multi-site chronic pain and CanUD. As pain is a complex trait and different type of pain may interact differently with CanUD, our finding for multi-site chronic pain is not sufficient to draw conclusions about the interaction between CanUD and specific kinds of pain or pain syndromes. Our definition of CanUD was based on any report of abuse or dependence either as an inpatient or outpatient. Participants in this study span a period of changing legal status and increasing use of marijuana, a major secular trend. Given the age of the participants  and SNP-based heritability (h2) was not statistically different , so case definition per the second classification was retained for further analysis . All individuals diagnosed under the first disease definition were also diagnosed under the second more inclusive definition. Controls were defined as individuals without any VA EHR ICD codes for cannabis dependence, cannabis abuse or cannabis use . The PGC cohort was as previously described and was made up of 16 cohorts with varying phenotype definitions and ascertainments10. A leave-one-out analysis was performed to remove the iPSYCH1 sample, leaving 18,370 cases and 304,838 controls for European and African ancestries in the remaining PGC/deCODE sumstats. An updated expanded iPSYCH2 cohort was then added via meta-analysis . We also included samples from MGB Biobank  and new data from the Yale–Penn cohort46 beyond the individuals already included in the PGC study . Table We used data release version 4 of the MVP. Linked and de-identified EHRs were queried using the Veterans Affairs Informatics and Computing Infrastructure to identify individuals with International Classification of Disease (ICD) codes for cannabis dependence or cannabis abuse   phase 3 panel and merged in an approach similar to that employed by the UK Biobank. Designation of broad ancestries was based on genetic assignment with comparison to 1KG reference panels47.Genotyping and imputation of MVP participants has been described previously10. This leave-one-out PGC meta-analysis contained 14,522 EUR cases and 298,941 controls and 3,848 AFR cases with 5,897 controls. This study includes new genotypes from iPSYCH (referred to as iPSYCH2), and all iPSYCH data (iPSYCH1 + 2) has been reprocessed. Pre-imputation quality control and imputation were performed on genotypes from the full set of genotyped individuals for iPSYCH1 and iPSYCH2 separately, using standard procedures for GWAS data. The iPSYCH1 samples were genotyped in 23 genotyping waves and thus additional steps were taken to eliminate potential batch effects. Only variants present in more than 20 waves and with no significant association with wave status were retained. Imputation was done using the pre-phasing/imputation stepwise approach implemented in EAGLE v2.3.548 and Minimac49, using the Haplotype Reference Consortium50 panel v1.0. GWAS of 4,733 EUR cases and 95,657 controls and was done on a merged set of best-guess genotypes with MAF >0.01 and imputation info score >0.8 (in both iPSYCH1 and iPSYCH2) using logistic regression with appropriate covariates , first ten positive controls and iPSYCH cohort of origin). A new Yale–Penn tranche was analyzed using PLINK 1.9 in unrelated individuals not previously included in any other GWAS or meta-analysis. This contributed 310 cases and 1,471 controls (EUR) and 271 cases and 666 controls (AFR). Finally, MGH Partners BioBank51 contributed 456 cases and 24,088 controls (EUR).MVP GWAS was conducted using logistic regression in PLINK 2.0 using the first ten positive controls, sex and age as covariates. Variants were excluded if call missingness in the best-guess genotype exceeded 20%. Alleles with MAF <0.1% were excluded in EUR, AFR and AMR. Alleles with MAF <1% were removed from EAS due to smaller sample size. The MVP data represented the largest and most diverse cohort with 22,260 cases and 423,587 controls (EUR), 14,946 cases and 97,580 controls (AFR), 2,774 cases and 35,515 controls (AMR) and 194 cases and 6,649 controls (EAS)  carried out in the study sample to adjust LD scores to enable calculation of SNP heritability in each ancestry using sample-specific LD scores. LDSC as implemented by the Complex Traits Genomics Virtual Lab56 was used to estimate genetic correlations57 to identify common genetic architecture across all 1,335 traits available for comparison. Additionally, LDSC was used to compare genetic correlations between CanUD and cannabis use (from a previously published study18).LDSC was used to calculate SNP-based heritability on the liability scale, using a lifetime population prevalence19 was used to generate cross-ancestry covariance scores using 1KG reference panels from EUR and AFR. This method was applied to calculate genetic correlations between the AFR CanUD generated in this study against traits from Fig. n count.POPCORN58. We conducted MR Egger analysis to test for the effect of horizontal pleiotropy.Several traits with significant genetic correlation with CanUD and high public health importance were selected for follow-up MR analysis in EUR ancestry datasets . These traits were first tested for polygenic overlap with CanUD; one trait did not survive this step (Alzheimer’s disease), and the remaining three traits moved on to MR analysis. MR was conducted using the TwoSampleMR package in R Studio20. The CanUD (target trait) GWAS data were conditioned on smoking initiation and cigarettes per day (covariate traits) GWAS data individually using the Genome-wide Complex Trait Analysis mtCOJO utility59. Output summary statistics from conditioned CanUD was then used to re-test the MR relationship between CanUD and lung cancer.mtCOJO was carried out to study possible confounding of smoking for CanUD. GWAS summary statistics for smoking initiation and cigarettes per day from the GWAS and Sequencing Consortium of Alcohol and Nicotine use Phase 2 study of EUR ancestry were used for smoking60 software were employed to use variant–gene expression associations to enrich GWAS variant findings for genes involved with CanUD. The TWAS models were trained using prior published evidence for gene expression from adult brain cortex33  and fetal brain frontal cortex34 , with each gene having estimated positive cis-heritability at nominal P < 0.01 and the corresponding predictive model achieving five-fold cross-validation R2 > 0.01 at a nominal P < 0.01. Using a weighted burden test60, we generated a Wald-type Z score for each gene–trait association, with transcriptome-wide significance defined at P < 2.5 × 10−6, the Bonferroni-corrected significance level across 20,000 tests. To ensure proper alignment to the genetic ancestry of the eQTL and GWAS cohorts, we use a reference panel from EUR individuals in 1KG61. The TWAS samples did not include any ascertainment for CanUD in the brain tissue used for analysis.Transcriptome-wide association studies (TWAS) and FUSION62. This permutation generates a null distribution to compare to the original TWAS Z score to quantify the significance of the expression–trait associations conditional on the SNP–trait effects at the locus60. For genes that passed both transcriptome-wide significance and the permutation test at P < 0.05 within 1 Mb of another significant gene, we conducted probabilistic gene-level fine-mapping using FOCUS to estimate 90% credible sets of genes that explain the trait association signal at a locus63. We conducted FOCUS fine-mapping across genes detected by models trained in either adult or fetal brain tissue.For every transcriptome-wide significant gene–trait association, we conducted a permutation test by shuffling the SNP-gene weights in the prediction model 10,000 times61. Genes with at least one significant eQTL were designated ‘eGenes’. We generated LD score annotations for 500-bp windows around lead eQTLs of eGenes from Genotype-Tissue Expression brain cortex (n = 205) and fetal brain frontal cortex (n = 201). We used Genotype-Tissue Expression to ensure similar sample sizes. We define the enrichment of SNP-based heritability as the proportion of heritability explained by a set of SNPs in the annotation divided by the proportion of all SNPs included in the annotation.To assess differences in enrichment of SNP-based trait heritability in the regions around eQTLs of adult and fetal expression, we employed stratified LDSC64 was used to perform EFA and CFA of CanUD and 14 additional traits of interest that were genetically correlated. For EFA, factor structures composed of one to ten factors were examined. EFA model fit was evaluated by the amount of cumulative variance explained by the overall factor structure, the SS loadings (SS loading ≥1) for each included factor and the proportion of explained variance accounted for by each of the individual factors . Traits with EFA factor loadings ≥0.20 were evaluated for optimal CFA model fit determined by conventional fit indices64. CFA models were estimated using diagonally weighted least squares estimation and a smoothed genetic covariance matrix. The 1KG phase 3 EUR reference panel was used for LD calculation47.gSEM65 for the joint analysis of the genome-wide association statistics of CanUD , AUD 66 and nicotine dependence 67. First, SNPs that were duplicated, had MAF ≤0.01 or had strand ambiguity were removed from the GWAS datasets. Of the 14,768,834 SNPs available from the GWAS meta-analysis of CanUD, 5,894,946 SNPs remained for the MTAG analysis after quality control. After the MTAG analysis with AUD and nicotine dependence, 3,540,940 SNPs remained. Significant variants were defined at P < 5 × 10−8.We applied the MTAG methodFurther information on research design is available in the Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41588-023-01563-z.Supplementary InformationSupplementary Tables 1–16 and Supplementary Figs. 1–7.Reporting Summary


Cotton fiber quality-related traits, such as fiber length, fiber strength, and fiber elongation, are affected by complex mechanisms controlled by multiple genes. Determining the QTN-by-QTN interactions (QQIs) associated with fiber quality-related traits is therefore essential for accelerating the genetic enhancement of cotton breeding. In this study, a natural population of 1,245 upland cotton varieties with 1,122,352 SNPs was used for detecting the main-effect QTNs and QQIs using the 3V multi-locus random-SNP-effect mixed linear model (3VmrMLM) method. A total of 171 significant main-effect QTNs and 42 QQIs were detected, of which 22 were both main-effect QTNs and QQIs. Of the detected 42 QQIs, a total of 13 significant loci and 5 candidate genes were reported in previous studies. Among the three interaction types, the AD interaction type has a preference for the trait of FE. Additionally, the QQIs have a substantial impact on the enhancement predictability for fiber quality-related traits. The study of QQIs is crucial for elucidating the genetic mechanism of cotton fiber quality and enhancing breeding efficiency. HoweverIn this study, we used a new R package called 3VmrMLM  develope22.1n=630) and grown in four environments representing the major cotton cultivation regions, Yellow River region (YER), Yangtze River region (YZR), northern Xinjiang region and southern Xinjiang region, respectively. Each environment contains two locations and two replicates. YER is represented by the cities of Shijiazhuang in Hebei Province  and Anyang in Henan Province . YZR was represented by the cities of Yancheng in Jiangsu Province  and Changsha in Hunan Province . Two adjacent fields in Shihezi, Xinjiang Province  represented the region of northern Xinjiang. South Xinjiang was represented by Kuche  and Alaer . Each line was grown with two random blocks and each block contained ~30 (YER and YZR) and ~60 (Xinjiang region) individuals. The field management is in strictly accordance with local planting standards.This study used a natural population including 1260 varieties of upland cotton from 3K-TCG panel including 3,278 accessions with 6,711,614 SNPs . Due to In each block, cotton bolls with uniform development conditions were harvested for testing the fiber quality with a high-volume instrument (HVI9000) at the Urumqi Center of Supervision and Testing of Cotton Quality, Chinese Ministry of Agriculture. Fiber length (mm), fiber strength (cN/tex), and fiber elongation rate (%) were utilized to estimate the best linear unbiased prediction values (two replicates for two years) using the lme4 module of the R programming language . After d2.2The 3VmrMLM method is a three-variance component mixed model method to detect and estimate all types of effects in GWAS. Our common genome-wide association analysis method is based on population structure and multi-gene background control and SNP fixed effect of single-marker association whole-genome scanning, which involves multiple tests. The 3VmrMLM method overcomes this limitation and greatly reduces the computational burden. It can compress the mixed model of five variance components into a mixed model of three variance components in main-effect QTNs detection, and compress the mixed model of 15 variance components into a mixed model of three variance components in QQIs detection.Before using the 3VmrMLM method, the R package 3VmrMLM and its corresponding R packages must be locally installed in the R program, and the phenotype file, genotype file, and population structure file need to be prepared. Noteworthy is the fact that genotype data must be organized in plink format. This method can manage the entire SNP marker set for main-effect QTNs and environmental interaction QTNs. Keeping only 5000 SNPs (interaction pairs) is preferable for interaction QTNs due to the calculation time. Therefore, how the 5000 SNPs are selected is crucial to the QQI results. Users have to alter particular parameters to accomplish their own detection objectives.2.3In this study, we used the 3VmrMLM method combining R and C++tools  to detec2.4Due to the “epistasis” method in the 3VmrMLM package needs a long running time, if all SNPs are operated, the work burden will be greatly increased, and the laptop will not be able to run. In order to save computing time and avoid missing significant loci, this study firstly screened the number of SNPs, and then carried out parameter modification and mapping analysis. The detailed steps are mainly divided into the following three steps:P < 0.01 were screened out from the intermediate results of main effect QTNs detection for each trait. A total of 5822, 5370 and 4269 SNPs were screened out for FL, FS and FE, respectively. PLINK v1.9 software was utilized to convert the genotype files containing 1,122,352 SNPs into Plink binary files, from which the genotypes of SNPs screened for each trait were extracted.In the first step, SNPs with In the second step, using the R package 3VmrMLM to detect QQIs with the specified parameters , and LOD = 3). TBtools v1.09 software was used to create a Circos diagram based on the results of QQIs .t-test  ‘TM-1’ genome CRI v1.0  of the phenotypic variation. Six QTNs contributed to PVE larger than 1.5%, of which 3.2A total of 42 pairs of QQIs were detected associated with the three fiber-quality traits, explaining 54.37% of the a cumulative PVE. Eight pairs of QQIs for FL, explaining 10.55% cumulative PVE, were identified with an average PVE of 1.32%, ranging from 0.27% to 5.69%. A total of 13 pairs of QQIs were detected in relation to FS, with PVE ranging from 0.23% to 5.55%, carrying an average PVE of 1.95% and cumulative PVE of 25.35%. For the trait FE, 21 pairs of QQIs were found, accounting for 18.47% of phenotypic variation, with an average PVE of 0.88% ranging from 0.36% to 2.17%  with the PVE of 5.69% and 0.30%, respectively; One pair of QQIs was found in FS (epiFS-A04-2 by epiFS-D07-3), with the PVE of 2.56%; Two pairs of QQIs were found in FE  with the PVE of 0.37% and 2.17%, respectively. A total of 13 pairs of type II QQIs were identified, including 3 pairs for FL, 6 pairs for FS, and 4 pairs for FE, with the cumulative PVE of 3.15%, 11.24% and 3.02%, respectively. The proportion of type III QQIs was higher than the other types, a total of 24 pairs of QQIs were detected, including 3 pairs for FL, 6 pairs for FS, and 15 pairs for FE, with the cumulative PVE of 1.41%, 11.56% and 12.91%, respectively , DD (loci interactions between Dt subgenome) and AD (loci interactions between At subgenome and Dt subgenome). Among the 42 pairs of QQIs, 14 pairs belonged to the AA types, explaining 22.41% of the cumulative phenotypic variation, with an average PVE of 1.60% that varied from 0.27% to 5.69%. The proportion of DD types was the lowest, only 7 pairs of QQIs were detected with the PVE ranged from 0.68% to 2.37%, explaining 1.26% of the phenotypic variation on average and 8.82% of cumulative phenotypic variation. A total of 21 pairs of QQIs were AD types, explaining 23.14% of the cumulative phenotypic variation, with an average PVE of 1.10% ranging from 0.23% to 3.78%  and one candidate gene (Gh_A10G071000) were detected as the epistatic QTNs. There being 8 main-effect QTNs named qFS10、qFS11、qFS19、qFS25、qFS26、qFS48、qFS53、and qFS63 were detected as epistatic QTNs in FS. For FE, six epistatic QTNs and two candidate genes were detected as main-effect QTNs.Among the detected QQIs, one epistatic hotspot was found in relation to FL which interacted with two QTNs  according to the genotype information-based population structure analysis, phylogenetic analysis and principal component analysis (PCA) . One indepiFE-D04-6, interacting with epiFE-D13-1, which was located in the same region of the gene Gh_D04G181300 reported previously in relation to FE . Mean FE values of AA and GG were 10.19% and 9.36% at epiFE-D04-6, mean FE values of AA and CC were 9.61% and 10.03% at epiFE-D13-1, respectively  in G4 subgroup, indicating that the superior allele was strongly selected in G4 subgroup (epiFE-D13-1 (CC) was strongly selected in G1 subgroup. A total of 27.27% of individuals carried superior allele of epiFE-D13-1 (CC) in G1 subgroup (epiFE-D04-6 and genotype of CC in epiFE-D13-1 (3.65%). Therefore, superior allele of combination of epiFE-D04-6 and epiFE-D13-1 (AACC) was strongly selected in G3 subgroup  was enhanced by the genotype of TT of epiFL-D03-1   was lower than that in their interaction (21.11%), so the dominant genotype combination (AATT) was strongly selected in G4 subgroup.The second example was the epistasis hotspot of 0G071000 . The dif3.4We compared predictability of each trait estimated from the main-effect QTNs, joint main-effect QTNs and QQIs through 10-fold cross validation Figure 444.1Gh_D11G206800, which corresponds to the previously confirmed gene Gh_D11G1929, to be highly expressed during fiber development from 5 to 20 days post anthesis (DPA)  affecting the expression of cell wall organization to regulate cell elongation  . We furtongation . The detA07G1758  which iser cells . Therefostrength . Therefoon to FE . ThroughepiFE-D04-6 and epiFE-D13-1, carrying the highest FE. The gene Gh_D04G181300 located on the candidate region of epiFE-D04-6, showing a dynamic change in 5-20DPA during the development of fiber cell. In addition, the transcriptome analysis showed that Gh_D04G181300 was highly expressed in both ovule development and fiber cell development, thus affecting cotton fiber elongation  was considerably higher than those of the other four subgroups (epiFL-A10-1 and epiFL-D03-1, we found that the superior genotype combination AATT was strongly selected in the G4 subgroup. Therefore, we speculated that the high FL in G4 subgroup was partly contributed by the superior genotype combination AATT. Growing upland cotton in this region is conducive to producing long FL plants. Future research can develop efficient molecular markers targeting these epistatic interaction QTNs to expedite the application of molecular marker-assisted selection in cotton breeding and enhance cotton breeding efficiency for fiber quality.Individuals in the G3 subgroup were predominantly from Xinjiang with the largest average of 9.69% of FE (In conclusion, the detection of QQIs is extremely important for the investigation of the genetic mechanism underlying cotton fiber quality-related traits. This study will further accelerate the process of epistatic interaction in the study of cotton fiber quality, help to dissect the genetic mechanisms of cotton fiber quality, and promote the breeding of upland cotton plants with excellent fiber quality.The original contributions presented in the study are included in the article/YC and LW designed the project and ZH analyzed the data and wrote the manuscript. HK, XL, RP, DZ and YX assisted in conducting data analysis. WW and YC provided the direction for the study and the correction of the manuscript. All authors contributed to the article and approved the submitted version.


Advancing age is the greatest risk factor for developing multiple age-related diseases. Therapeutic approaches targeting the underlying pathways of ageing, rather than individual diseases, may be an effective way to treat and prevent age-related morbidity while reducing the burden of polypharmacy. We harness the Open Targets Genetics Portal to perform a systematic analysis of nearly 1,400 genome-wide association studies (GWAS) mapped to 34 age-related diseases and traits, identifying genetic signals that are shared between two or more of these traits. Using locus-to-gene (L2G) mapping, we identify 995 targets with shared genetic links to age-related diseases and traits, which are enriched in mechanisms of ageing and include known ageing and longevity-related genes. Of these 995 genes, 128 are the target of an approved or investigational drug, 526 have experimental evidence of binding pockets or are predicted to be tractable, and 341 have no existing tractability evidence, representing underexplored genes which may reveal novel biological insights and therapeutic opportunities. We present these candidate targets for exploration and prioritisation in a web application. For instance, the UK Office for National Statistics reported that the proportion of the population aged over 85 is projected to increase from 2.5% in 2020 to 4.3% by 20502. However, the number of years in good health – the “healthspan” – is not increasing at the same pace3 and people are experiencing an increasing number of years of ill-health in later life. More than half of people over 65 in the UK suffer from multiple long-term health conditions4 known as multimorbidity, for which it is common for people to be taking five or more medications, known as polypharmacy5. The traditional model of tackling diseases independently during research, drug development, clinical trials, and treatment may not be best serving these patients, who represent an increasingly large proportion of the general population. Advancing age is the greatest risk factor for developing multimorbidity, suggesting that biological ageing processes play a pathogenic role. A Geroscience approach, one that aims at tackling combinations of diseases via their common underlying ageing pathways, has been proposed as a way to treat and prevent age-related morbidity more effectively whilst potentially reducing the burden of polypharmacy8.Life expectancy is increasing globally, bringing with it the need for new approaches and therapeutics to promote healthy ageing1. The rate of decline relative to chronological age varies between individuals, and there is evidence from animal models and humans that this can be modified through interventions7. Specific biological processes are thought to contribute to ageing and the pathology of age-related diseases, termed the Hallmarks of Ageing9 and comprise: Telomere shortening, epigenetic modifications, genomic instability, reduced proteostasis, altered nutrient sensing, mitochondrial dysfunction, cell senescence, stem cell exhaustion and altered intercellular communication, with increased systemic inflammation a key component of the latter.Ageing is associated with time-dependent functional decline, initially manifesting as subclinical physiological changes in the body, progressing to more systemic changes, and ultimately defined by disease conditions and multimorbidityet al.10 found significant genetic overlap between 8 age-related diseases and parental lifespan, based on 961 genome-wide significant variant-trait associations in the GWAS catalog. The authors identified 12 multi-trait loci, including variants relating to inflammation, obesity, blood lipid levels, DNA repair mechanisms, and telomere maintenance. For instance, Apolipoprotein E (APOE) is involved in lipid transport and neural health, and is strongly linked to multiple age-related traits including Alzheimer’s disease, cardiovascular disease, stroke, and longevity10.In support of generic mechanisms driving multimorbidity, previous genetic studies have found that age-related diseases are genetically correlated, and that genes with multi-trait associations often relate to biological processes that are implicated in ageing. Belloy et al.11 identified common genetic associations between age-related diseases using a data-driven approach. Using self-reported disease data for UK Biobank (UKBB) participants aged up to 70 years, diseases were clustered based on age-of-onset profiles. One cluster of diseases showed a rapid increase in incidence after age 40, and contained cardiovascular diseases, diabetes, osteoporosis and cataracts. A second cluster shared a slower age-related rate of increase from age 20, including musculoskeletal and gastrointestinal diseases, anaemia, deep vein thrombosis, thyroid problems and depression. Two final clusters contained diseases with childhood-onset (primarily inflammatory diseases) and uniformly distributed age-of-onset (respiratory and infectious diseases). GWAS performed on each disease found a high level of genetic similarity within clusters of diseases with similar age-of-onset profiles, even after controlling for shared disease categories and co-occurrences. Furthermore, the diseases in clusters with age-dependent onset profiles were associated with 581 genes, which were significantly enriched in known ageing-, longevity-, and senescence-related genes.Dönertaş et al.12 used deep learning models including omics, literature, and key opinion leader scores from multiple data sources to predict a list of 484 genes implicated in a set of 14 age-associated diseases. Well-known age-related genes were found, along with a number of novel genes. A final set of 9 genes was prioritised with strong links to inflammation and epigenetic programming.Pun 6. Although a number of promising novel drug targets have been explored for the treatment of multimorbidity, as well as repurposing existing drugs such as Metformin14, there has so far been limited success in clinical trials7.Whilst this biological relationship between ageing and multimorbidity suggests a potential strategy for therapeutic intervention via shared pathways, translating this biological understanding to clinical benefits in patients presents a challenge15, we focus on a genetics approach to identifying potential drug targets implicated in multiple ageing-related diseases. We use the Open Targets Platform16 and Open Targets Genetics Portal17 to perform a systematic analysis of 1,394 genome-wide association studies (GWAS) mapped to a curated list of age-related diseases and traits to identify genetic signals that appear to be shared between two or more of these traits   Fig. .Fig. 1Ovet al.18 . Terms categorised as genetic, familial or congenital disease , as well as pregnancy or perinatal diseases were removed as these are less likely to be ageing-related traits. We additionally excluded cell proliferation disorders; whilst some cancers are prevalent amongst older people, cancers have distinct genetic and environmental disease pathways that are not in the scope of the present study. A full list of the resulting 414 traits and corresponding EFO codes can be found at Figshare (All Traits Details)20.An overview of the genetic analysis is illustrated in Fig. https://genetics.opentargets.org/) with a sample size  of at least 2,000 for which the reported traits mapped to these age-related traits of interest, or their descendants in the ontology. This resulted in 1,394 GWAS studies representing 160 different traits mapping to 30 of the 34 curated age-related traits (SI Table p < 5 × 10−8).We retrieved all GWAS studies included in Open Targets Genetics , otherwise overlap of variants derived from Linkage Disequilibrium (LD) expansion or fine mapping (see Methods).Around 12% of hits  were only identified in a single GWAS. The remaining associations were grouped into 3,158 clusters of which 2,152 contained associations to one trait and 1,006 clusters involved more than one trait.This approach aims to cluster together GWAS hits that correspond to a single genetic signal. However, in some cases, the resulting clusters containing multiple associations may still include multiple distinct genetic signals. To investigate whether clusters could be subdivided further, we applied, to each cluster, a community detection algorithm that aims to identify subclusters with weak co-localisation or LD evidence across subclusters and strong evidence within subclusters (see Methods). Most clusters consisted of just one community  or two communities . The largest number of communities within a single cluster was 9 (cluster ID 21) consisting of 299 nodes from 15 traits and was most strongly associated with the gene encoding APOE.Using these clusters of genetic associations to age-related traits, we tested whether the overlap in genetic signals between pairs of traits was larger than expected by chance given the total number of genetic signals linked to each trait  Fig. . Overall21. As expected, metabolic syndrome has significant overlaps with all these related traits, as well as age-related macular degeneration, gait measurement, and grip strength measurement. The next most significant overlap is between lean body mass and grip strength measurement, the diagnostic measurements used to define sarcopenia, a common ageing-related condition characterised by loss of skeletal muscle mass, strength and function22. This is followed by the highly correlated traits lean body mass and obesity, as well as type 2 diabetes and obesity.Most of the significant pairwise overlaps are consistent with previously identified relationships between ageing-related diseases and traits, indicating that the clustering method captures relationships between correlated traits. The most significant overlap is between lipid measurement and metabolic syndrome. Metabolic syndrome is a combination of metabolic abnormalities including altered blood lipid levels, hypertension, obesity, and insulin resistance, which are risk factors for type 2 diabetes and cardiovascular disease24, and age-related macular degeneration with metabolic syndrome and type 2 diabetes. There is also a significant overlap between loci associated with heel bone mineral density and osteoporosis. Gait measurement and grip strength measurement significantly overlap and are known to negatively correlate with multimorbidity26. Atherosclerosis is a known life-threatening comorbidity of COPD, and while these diseases are currently treated separately, recent work has proposed identifying and treating shared underlying mechanisms27; we find shared genetic associations that could shed light on such mechanisms.Other overlapping traits reflect known clinical associations, including hypertension with chronic kidney disease and type 2 diabetes29. We also find a significant overlap between osteoarthritis and glaucoma. While inflammatory forms of arthritis are thought to increase the risk of glaucoma due to intraocular pressure, and a possible common autoimmune-mediated pathological pathway has been proposed for rheumatoid arthritis and glaucoma31, there is no established link between osteoarthritis and glaucoma.We also find novel correlations between age-related diseases and traits. We find a significant overlap between adult-onset asthma and rheumatoid arthritis; some epidemiological studies have found a positive association between asthma and rheumatoid arthritis, but the relationship is poorly understoodAPOE and involves 9 age-related traits including age-related macular degeneration, Alzheimer’s disease, atherosclerosis, as well as longevity.The single lead variant associated with Lewy body dementia  is part of cluster 21 that is linked to 32, the combined analysis provides more power to identify associations. Of the 21 clusters that include a longevity trait, most were associated with the combined study of combined ageing (13/21), whereas 4 contained only longevity and 4 contained only parental lifespan.Longevity has significant overlaps with healthspan, atherosclerosis, stroke, obesity, osteoarthritis, type 2 diabetes, and lipid measurement. The longevity associations are derived from GWAS on parental lifespan (13 studies), survival to exceptional age (7 studies), and 1 multivariate analysis of ageing traits . While parental lifespan and longevity have been found to have distinct genetic associationsThese results are consistent with previous findings on the shared underlying genetics of ageing-related diseases and traits. We hypothesise that genes implicated with multiple ageing-related traits could represent shared aetiology that may relate to underlying ageing processes.33 (Methods). Of the 1,006 clusters involving more than one trait, 796 (79%) contain at least one predicted causal gene (L2G score > = 0.5) with 178 of these supported by co-localisation with protein quantitative trait loci (pQTL) or gene expression quantitative trait loci (eQTL). Overall, there are 1,021 predicted causal genes linked to at least one multimorbidity cluster, of which 995 are protein-coding, which we refer to as the “TargetAge” gene set. Overall, 290 (29%) of TargetAge genes are annotated to at least one Hallmark of Ageing (p = 1.40 × 10−6).We mapped each independent genetic association cluster to possible causal genes using the Open Targets Genetics ‘locus-to-gene’ (L2G) score for each locus in the clusterMPPED2, APOB, LDLR, TBX3, ZFHX3, BCL2L11, SMAD3, and IRS1) linked to three clusters, and two genes, PPARG and LRMDA, are linked to four clusters.The majority of TargetAge genes are linked to one  or two clusters . There are eight genes (IRS1 (insulin receptor substrate 1) and PPARG (peroxisome proliferator activated receptor gamma) have previously been linked to ageing and are included in GenAge, a manually curated database of ageing-related genes due to longevity-altering effects in model organisms34. Knockout of the gene homologous to IRS1 resulted in increased lifespan in both mice35 and drosophila36. PPARG is an important regulator of several ageing-related pathways and has genetic links to type 2 diabetes, atherosclerosis, and longevity; mice with lowered expression of the homologous gene have reduced lifespan37. A further four genes have links to the Hallmarks of Ageing, including TBX3 (T-box transcription factor 3) a regulator of cellular senescence38. SMAD3 (SMAD family member 3) is a regulator of inflammation and an inhibitor of PPARG expression39; decreased expression of the orthologue Smad3 has been linked to ageing, neuroinflammation, and neurodegeneration in mouse models40. LDLR (low density lipoprotein receptor) and APOB (apolipoprotein B) are involved in proteostasis and nutrient signalling. APOB has been linked to longevity in humans and mice, and may play a role in the pro-longevity effects of dietary restriction41.Of the genes linked to more than two clusters, MPPED2 , ZFHX3 (zinc finger homeobox 3), BCL2L11 (BCL2 like 11), and LRMDA (leucine rich melanocyte differentiation associated). Although it does not have a known role in inflammation, a MPPED2 polymorphism has been associated with altered systemic inflammation and adverse outcomes in trauma patients42. The transcription factor ZFHX3 is associated with atrial fibrillation, an ageing-related condition, and has a potential role in inflammation44. LRMDA is involved in melanocyte differentiation, and BCL2L11 is a mediator of apoptosis and is associated with tumorigenesis45.The remaining four genes that were linked to more than two clusters, but do not have established links to GenAge or the Hallmarks of Ageing, are 34), and cellular senescence . The third is a set of 4,527 genes annotated with Gene Ontology (GO) biological process terms representing each of the Hallmarks of Ageing (see Methods).We compared the TargetAge gene set with three sets of genes with known links to ageing. Two are manually curated databases of human genes linked to ageing or longevity , and 34 (3.4%) are in CellAge (representing 12% of the CellAge database) . Whilst these significant overlaps indicate shared biology coverage between TargetAge, GenAge, and CellAge, the sets are mostly distinct, which suggests that there are elements of unique biology that are being captured by each set.The most highly represented hallmark is the immune inflammatory response  Fig.  .ESR1), is the target of an investigational proteolysis-targeting chimeras (PROTAC) treatment for Metastatic ER + /HER2- Breast Cancer. Targets with existing drugs may have efficacy and safety information available and may represent potential drug repurposing opportunities.We used the Open Targets tractability assessment to explore the drug development opportunities within the TargetAge gene set Fig. . Of the 47.For the development of a small molecule drug, targets must have a suitable binding site. There is evidence of ligand binding for 202 TargetAge targets (categorised as “Discovery Precedence”), and a further 61 targets are predicted to have a binding pocket or are members of the druggable genome (categorised as “Predicted Tractable”) (see Methods). The druggable genome represents the subset of human genes thought to be amenable to drug development, including those closely related to drug targets, secreted proteins, and members of key drug target protein familiesFor a therapeutic antibody approach, a target is categorised as “Predicted Tractable” if its subcellular localisation is accessible to an antibody, such as location in the plasma membrane. There are 324 high confidence “Predicted Tractable” targets that are annotated to accessible locations based on high confidence experimental evidence, while 158 medium confidence targets are either annotated with medium confidence evidence or have predicted Signal Peptide or Trans-membrane regions (see Methods).48. There are literature reports of successful PROTAC approaches for 28 targets, and a further 772 represent possible PROTAC opportunities based on the PROTACtable Genome assessment48, which considers the cellular location, evidence of ubiquitination and small-molecule ligand binding sites, and the availability of protein half-life information (see Methods).Proteolysis-targeting chimeras (PROTACs) are an emerging drug modality in which proteins are targeted for ubiquitin-directed degradation50. High quality chemical probes are available for 38 TargetAge targets, characterised by the expert-curated Chemical Probes Portal49, the precompetitive pharmaceutical collaboration Open Science Probes51, or the public-private partnership Structural Genomics Consortium49. Of these, 11 targets do not have existing drugs in clinical development, representing potential novel drug discovery opportunities  TargetAge genes are the target of an approved or investigational drug. A further 526 (53%) have experimental evidence of binding pockets or are predicted to be tractable by small molecule or antibody modality approaches. The remaining 341 (34%) have no existing tractability evidence, representing underexplored genes which may reveal novel biological insights and therapeutic opportunities.We systematically combined 1,394 GWAS of age-related traits to identify clusters where one or more of these traits shared a common genetic signal. To develop the genetic clusters, we made use of genetic co-localisation (when summary statistics were available and credible sets overlapped) and LD-expansion (in the absence of summary statistics) from Open Targets Genetics. We identified 1,006 clusters in which a shared causal variant is implicated in multiple age-related traits. From these clusters, we created the TargetAge gene set of 995 candidate causal genes, of which 29% have a known annotation to at least one Hallmark of Ageing. They are particularly enriched in immune response pathways; dysregulation of these pathways and chronic inflammation, a hallmark of ageing referred to as immunosenescence, is thought to contribute to age-related morbidity. This set has a statistically significant overlap with the manually curated ageing-related gene sets GenAge and CellAge, with evidence of shared biological processes, but 935 of these genes are novel.The TargetAge genes and genetic analysis outputs are presented in an interactive web application Fig. . The mulThe application facilitates the exploration and prioritisation of potential drug development opportunities for age-related multimorbidity. Some may represent drug repurposing opportunities: 13% of TargetAge genes are targeted by drugs with investigational or approved indications. A further 18% have experimental evidence of binding pockets, and a further 34% are predicted tractable either by small molecule or antibody therapeutics. Of these, 11 targets have high quality chemical probes already available and no existing drugs in clinical development. The remaining 34% have no existing tractability evidence, representing underexplored genes which may reveal novel biological insights and therapeutic opportunities. Together this analysis suggests there is substantial underexploited opportunity for development of drugs for age-related multi-morbidities.THRB) - one of several receptors for thyroid hormones - in cluster 1307. Overstimulation of this receptor by thyroid hormone can cause hyperthyroidism53. In adults, hyperthyroidism is associated with increased incidence of atrial fibrillation - with older patients at greater risk54 - as well as osteoporosis and increased risk of bone fracture, although the underlying mechanism is not fully elucidated55. The combination of atrial fibrillation and heel bone mineral density is represented in a further 14 clusters.Some clusters identified in this analysis reflect established relationships between commonly occurring comorbidities. For example, a locus associated with atrial fibrillation and heel bone mineral density is linked to thyroid hormone receptor beta (EDNRA), the target of several approved small molecule drugs for pulmonary artery hypertension and type 2 diabetes indications, suggesting a potential repositioning opportunity for other cardiovascular diseases. Another cluster involving vascular diseases and stroke is linked to phospholipid phosphatase 3 (PLPP3). This gene is thought to play a role in vascular homeostasis through negative regulation of pro-inflammatory cytokines, leucocyte adhesion, cell survival and migration in aortic endothelial cells56. This locus co-localises with eQTLs in monocytes, which is consistent with a functional role in inflammation and vascular disease, and PLPP3 is predicted tractable by an antibody therapeutic approach.We note several clusters of cardiovascular diseases linked to a common therapeutically actionable target. For instance, cluster 209 represents an important locus for cardiovascular diseases, including coronary artery disease, peripheral arterial disease, and large artery stroke, and coronary atherosclerosis. The locus is strongly linked to the gene encoding endothelin receptor type A (PHACTR1). A study by Gupta et al. identified this as the causal variant for associations with five vascular diseases, with a putative mechanism acting through distal regulatory effects on endothelin-1 (EDN1), a gene located 600 kb upstream of PHACTR157. TargetAge replicates this association: cluster 644 links this variant to coronary artery disease, myocardial infarction, intermediate coronary syndrome, and coronary atherosclerosis. Furthermore, PHACTR1 is implicated in a second cluster, which is associated with ischemic stroke, large artery stroke, and hand grip strength in addition to coronary artery disease and myocardial infarction.In some cases, shared genetic associations may represent distal regulators of the causal gene. Cluster 644 involves a common non-coding variant rs9349379 in the third intron of phosphatase and actin regulatory protein 1  with type 2 diabetes (T2DM) risk, metabolic syndrome, and osteoarthritis. For example, FILIP1), implicated in a locus associated with increased lean body mass and increased risk of osteoarthritis (cluster 220), which is highly expressed in heart and skeletal muscle tissue, and is predicted tractable by a therapeutic antibody. We also identified shared targets that were not predicted tractable via small molecule or antibody approaches, but potentially tractable by proteolysis-targeting chimeras (PROTACs) - an emerging drug modality48. An example of the latter is CMIP (c-Maf inducing protein) - a negative regulator of T-cell signalling60. CMIP is linked to cluster 57, associated with lower triglycerides, higher adiponectin , lower risk of T2DM, and lower risk of metabolic syndrome.Another example of a shared target is Filamin A interacting protein  and removing connections between loci that are unlikely to share a causal variant despite sharing some overlapping tag variants . However, studies with summary statistics represent only around 10% of the GWAS studies available for the investigated ageing-related traits. Increased availability of comprehensive summary statistics would therefore improve our ability to distinguish overlapping but distinct signals. Community detection and visual inspection can help evaluate whether an individual cluster represents a shared genetic signal; the presence of multiple communities within the cluster may suggest that it includes distinct genetic signals. Furthermore, our findings may be biased to European populations due to the bias of the underlying data, although we expect the underlying biological mechanisms implicated to be relevant across human groups. Details of individual GWAS studies contributing to each cluster can be explored in the web application, including the sample size and ancestry of the study and replication populations. Where clusters contain multiple associations for each trait, this indicates that the association has been replicated in multiple studies.62. Such Geroscience, multimorbidity focussed approaches are relevant beyond age-related diseases, and the methodology described here could be applied to other clinically relevant combinations of diseases thought to share common genetic or biological pathways.The methodology described here demonstrates one way in which large-scale tools such as Open Targets Platform and Open Targets Genetics can be used to systematically combine evidence from difference sources and use co-localisation data at scale for multiple diseases and traits. Rather than understanding and treating ageing-related diseases seen in multimorbid patients in isolation, there is growing evidence that better health outcomes may be achieved by recognising that diseases often co-occur non-randomly around common genetic, biological, or environmental pathwaysWe have shown that our approach is able to highlight a range of opportunities both in terms of existing therapeutic agents against linked targets and also novel targets which might allow treatment for multimorbidity. In the present study, we have not explored the causal mechanisms linking the associated SNPs to the increased or decreased risk of each ageing-related outcome. This is an important next step for exploring any potential therapeutic or repurposing opportunities. For the subset of loci that colocalise with pQTLs and eQTLs, the relationship between the gene product and the outcome can be inferred from the direction of effect on the colocalised protein expression or abundance. This indicates whether a therapeutic approach would require activation or inhibition of the gene product, and whether any of the existing drugs would be suitable for repurposing. Individual clusters of interest can be interrogated in this way using the information presented in the application and in the Open Targets Platform and Genetics Portal. It will be important to develop tool molecules for those novel targets identified in order to better understand their biology and to validate their possible role in disease. Ultimately, clinical trials will be required to fully validate the associated proposed hypotheses in an ageing and multimorbidity context.https://platform.opentargets.org/downloads)16 and Open Targets Genetics version 210608 (https://genetics-docs.opentargets.org/data-access/data-download)17. From Open Targets Platform, targets were retrieved for which there is GWAS evidence linking the gene to any of the age-related trait EFO codes, or their descendant terms in the Open Targets EFO slim, excluding terms that contain the word “juvenile” or fall under the therapeutic areas “genetic, familial or congenital disease” (OTAR_0000018), “pregnancy or perinatal disease” (OTAR_0000014), or “cell proliferation disorder” (MONDO_0045024). For a full list of EFO codes, and the corresponding number of GWAS and genome-wide significant associations, see Figshare (All Traits Details)20. For all the GWAS studies contributing to this evidence, study information and lead variants were retrieved from Open Targets Genetics 20.Target and GWAS data were obtained from Open Targets Platform version 22.02  expansion and fine-mapping expansion.2 > = 0.7). In Open Targets Genetics, LD is calculated for all studies using the 1000 Genomes Phase 3 (1KG) genotypes as a reference. Where ancestry information is known for the GWAS study population, the most closely matching 1KG super-population is used - or a weighted-average across relevant super-populations for mixed ancestry study populations - otherwise European ancestry is assumed.Where summary statistics are not available, the tag variants include all those in LD with the lead variant (r33 (https://genetics-docs.opentargets.org/our-approach/assigning-traits-to-loci). In brief, where summary statistics were available, Genome-wide Complex Trait Analysis Conditional and Joint Analysis  was used to identify conditionally independent loci  using genotypes from the UK Biobank population down-sampled to 10 K study participants as the linkage-disequilibrium (LD) reference for the conditional analysis. Approximate Bayes factors were computed using the conditional summary statistics and posterior probabilities (PP) were derived from the Bayes factors for all SNPs within a ± 500Kb window assuming a single causal variant. Where summary statistics were not available, we used the Probabilistic Identification of Causal SNPs (PICS) method64 with LD from 1000 Genomes phase 3 data to estimate the PP for each variant. In both cases, any variant with a PP > 0.1% in the credible set is retained.Details of fine-mapping conducted for Open Targets Genetics are provided elsewhereWe used two methods to determine whether associations from different GWAS studies may share a causal variant and therefore represent the same signal, depending on the availability of full summary statistics for those studies.65. For each locus, this method integrates over evidence from all variants within a ± 500Kb window in each study to evaluate which of these four hypotheses is most likely: no association with either trait (H0), association only with trait 1 (H1), association only with trait 2 (H2), association with both traits via two independent SNPs (H3), or association with both traits through a shared causal SNP (H4). We use a cut-off of H4 > = 0.8 to define the association for study 1 and study 2 as sharing the same causal variant.Where summary statistics are available, Open Targets Genetics co-localisation analysis is usedFor most cases, summary statistics are not available for one or both studies. In this case, for lead variants less than 500Kb apart, the associations are considered to represent the same signal if at least one of the tag variants is shared between the two lead variants. Using a more stringent overlap criterion increased the overall number of clusters and decreased the number of clusters involving more than one age-related trait, but does not substantially affect the structure of the graph SI Fig. . When coGWAS association overlap, above).We construct an undirected, unweighted graph in which each node is a trait-associated locus from a single GWAS study, represented by the GWAS study and the lead variant. Nodes are connected by an edge where these genetic associations may share a causal variant, either through co-localisation analysis (where summary statistics are available) or tag variant overlap  with default parameters. To identify substructure within each cluster, which may indicate separate signals, we identify communities using “cluster_louvain” implementation of the Louvain community detection method with default parameters67.Graph construction and analysis was carried out in R (version 4.0.2) using igraph (version 1.2.6) (Csardi and Nepusz 2006) and visnetwork (version 2.0.9)fisher.exact in R. P-values adjusted for multiple testing (406 possible combinations of 29 traits) were obtained using BH  correction implemented in the p.adjust function68.To test the statistical significance of the genetic overlap between each combination of traits, raw p-values were obtained using one-sided Fishers exact test for each pair, implemented using 33. L2G is a machine learning method that combines predictive functional genomics features – including predicted pathogenicity, expression quantitative trait loci (eQTL), protein quantitative trait loci (pQTL), genomic distance, and regulatory regions – and outperforms models based on genomic distance alone70. This score ranges from 0 to 1 and is assigned using a supervised machine learning model, which is trained on 445 gold standard GWAS loci with high-confidence causal genes. We only consider genes with an L2G score of at least 0.5 and assign each locus to the gene with the highest L2G score.Loci were assigned to likely causal genes using the Open Targets Genetics locus-to-gene (L2G) score34. Human genes are included in the database if there is experimental evidence linking the gene to ageing through gene manipulation experiments in human, mammal, or animal models.GenAge is a manually curated database of genes thought to be involved in ageing or longevity that includes 307 human genes (GenAge Human) and 2,205 genes from model organisms (GenAge Models)46. Cellular senescence is one of the pathways associated with ageing and age-related pathology, and a major target for therapeutic intervention71.CellAge is a manually-curated database of 279 genes found to induce or inhibit cellular senescence through gene manipulation experiments in human cell models9. This includes causes of cellular damage , responses to damage , and processes that lead to the ageing trait . We curated a subset of Gene Ontology (GO) biological process terms that fall under each of the hallmarks of ageing  and “Predicted Tractable” if the target is predicted to have a binding pocket (drugEBIlity score > = 0.7) and/or is a member of the druggable genome.For antibody modality, targets categorised as “Predicted Tractable high confidence” are localised to the plasma membrane, extracellular matrix, or secreted, according to high confidence “Subcellular location” terms in UniProt or “Cellular component” terms in GO. “Predicted Tractable Medium to low confidence” targets are annotated to these locations with medium confidence or have predicted Signal Peptide or Trans-membrane regions.For PROTAC modality, targets with literature reports of successful PROTAC degrader are classified as “Literature Precedence”. Targets are classified as “Discovery Opportunity” if they meet the following criteria: evidence of a ubiquitylation site ; available experimental data on protein half-life; small-molecule ligand binders (≥10 μM activity reported in ChEMBL), are secreted, extracellular, or located in the cell cytoplasm, cytosol or nucleus (“Subcellular location” terms in UniProt or “Cellular component” terms in GO).https://www.thesgc.org/chemical-probes) and through Open Science Probes (https://www.sgc-ffm.uni-frankfurt.de/) are open access with no restrictions on use and are required to meet the following criteria: in vitro potency of < 100 nm, > 30-fold selectivity compared to related proteins within the same target family, demonstrated on-target effects in cells at < 1 μM, no PAINS elements, and (more recently) an inactive close analogue suitable for use as a control49. The Chemical Probes Portal  provides expert guidance and ratings for chemical probes; probes are included in Open Targets if they receive a rating of 4 or 3 stars, indicating a recommended or best available probe for a target.Information on available high quality chemical probes is retrieved through Open Targets. Chemical probes released by the Structural Genomics Consortium , structure-activity relationships (SAR), the availability of inactive analogues, and pan-assay interference compound (PAINS) predictionSupplementary Information


We demonstrate the benefits of our solutions at the example of single-step models which make repeated use of this kind of multiplication. Targeting modern Nvidia® GPUs as well as a broad range of CPU architectures, our implementation significantly reduces the time required for the estimation of breeding values in large population sizes. miraculix is released under the Apache 2.0 license and is freely available at https://github.com/alexfreudenberg/miraculix.In the last decade, a number of methods have been suggested to deal with large amounts of genetic data in genomic predictions. Yet, steadily growing population sizes and the suboptimal use of computational resources are pushing the practical application of these approaches to their limits. As an extension to the C/CUDA library  Over the past 15 years, the incorporation of genomic information has become essential for ensuring progress in breeding . A routiG and the pedigree-based relationship matrix A into a generalized relationship matrix H. Large population sizes used in animal breeding programs, ranging from tens of thousands to millions of individuals, have motivated research in computational strategies to solve the associated mixed model equations (MME) efficiently through the use of high-performance computing (HPC) techniques. One of the proposed approaches is the algorithm for Proven and Young Animals (APY), which approximates the inverse of the GRM, G−1, through genomic recursion on a subset of core animals (G using the Woodbury decomposition. The resulting models were coined single-step GT(A)BLUP models  model  has gain animals . As an a animals  and, secP models . Additio inverse .Considering the computational aspects of these approaches, the use of highly-optimized sparse matrix operations has been established, thanks to the sparse characteristics of the pedigree-based relationship matrix. Additionally, established iterative-solver algorithms  can be employed in the resulting equation systems  to avoid® Math Kernel Library (MKL) and PARDISO  operations explicitly . Interfaces to call the library from higher-level languages such as Fortran, R and Julia are provided. Through the modular structure of the miraculix library, which also supplies functions for the calculation of G, the code should be easily modifiable by researchers and practitioners interested in accelerating computations in other BLUP models  of ng genotyped animals. Furthermore, p denotes the vector of allele frequencies and the subtraction of M.We consider the commonly encountered operation of multiplying the centered SNP matrix Z with Λ can be reformulated intoConsidering an arbitrary matrix Since subtracting the matrix Λ and Z and Z′ cannot be multiplied with the same matrix because they have different dimensions. Due to the low cost of SNP genotyping, the matrix M can have extremely large dimensions, capturing the genomic information of millions of animals. Furthermore, whereas Λ is a regular matrix of double-precision, the SNP matrix is usually stored in a compressed format to save memory. For instance, the PLINK 1 binary file format stores the genotypes of four individuals in eight bits (corresponding to one byte), utilizing that one entry of M only requires two bits of storage. This compressed data format prevents naive calls to BLAS routines, and decompressing it explicitly is inefficient and increases memory requirements. Only recently, the problem of matrix multiplication of mixed input data types has gained attention  to reduce access times to repeatedly processed data. While infrequently used data can be stored in the random access memory (RAM) or even on the disk, accessing it over the memory bus combined with the lower clock cycles of the RAM compared to the CPU dramatically slows down the execution of the program. While low levels of cache close to the core allow faster memory reads, they come with lower capacity  for a SNP, any vector 5 = 243 double-precision values of 64 bits and the L1 cache in modern CPU architectures typically holds between 32 and 96 KB. Since the hash table of the different values of x only needs to be computed once for every five-row tile of Λ, we keep register instructions to a minimum. Furthermore, compressed matrix values are loaded into integer registers whereas real values are stored in SIMD registers. The implementation aims to optimize load operations and store operations. For instance, if SIMD registers of 256-bit width are available, one entry of the hash table contains a vector of four double-precision floating-point values.It is worth noting that at least 16 of these tables fit into the L1 cache because each hash table holds 3M and Λ into chunks along the column axis and row axis respectively. Finally, the results of each thread are united by a single reduction operation at the end that computes the sum of all individual results.The computation is parallelized among the available processor cores by splitting 5codes encoding, the centering can actually be included in the hash table for the operation ZΛ, meaning that instead of holding the possible values of m′λ, the hash table can store the centered valuesAs discussed above, genotype centering is not a bottleneck due to its low complexity. Thanks to the structure of the ′λp at this point further reduces the number of memory accesses and decreases numerical accumulation errors.Subtracting 2 ⋅Algorithm 15codes algorithm for the multiplication of five columns of SNPs M with a vector λ of length 5. The multiplication of five columns of ′M is analogous. Note that the variable idx in the algorithm is smaller than 243. For a general number of SNPs ns, five columns of M are multiplied at a time.Data: Compressed SNP matrix Result: Genotype matrix multiplication λx = M1/* Compute and store the dot products of λ with all possible SNP vectors */2 form ∈ {0,1,2}5 do3   idx ← m1 × 30 + m2 × 31 + m3 × 32 + m4 × 33 + m5 × 344   /* Compute and store m′λ*/5   table[idx] ← m1 × λ1 + m2 × λ2 + m3 × λ3 + m4 × λ4 + m5 × λ56 end7/* ComputeλMby looking up the realization ofmin the matrixM. */8 for j ← 1 to ngdo9   key ←Mj,1 × 30 + Mj,2 × 31 + Mj,3 × 32 + Mj,4 × 33 + Mj,5 × 3410   x[j] ← table[key]11 endPseudo-code for the ® GPUs, we also implement a matrix multiplication routine in CUDA, in which we extend the CUTLASS library  only once at start-up time. To our knowledge, this is the first implementation of matrix multiplication of 2-bit integers with double-precision floating-point values, which we designed in parallel to the recent work of To make use of the powerful HPC capabilities of modern Nvidia library  in its v threads . CUTLASSM of low dimension which are iterated over. For instance, transposing sub-matrices of dimensions 16 by 16 in PLINK 1 binary format would allow distributing the transpose operation in a warp of threads on a GPU. However, thanks to the compressed data storage, we are not memory-bound with the current number of genotyped animals and SNPs, and we, therefore, choose to transpose M as a whole during start-up and store it separately to reduce computation time associated with transposition. For instance, the dataset of 2.61 m animals with 47 k SNP markers we use in this article for testing purposes only requires about 57 gigabytes of RAM for both M and M′ combined.Since both the CPU and GPU approaches exploit a compressed storage format for the SNP matrix, the question arises of how to efficiently calculate the transposed matrix product Single-step models in animal breeding programs commonly comprise hundreds of thousands or even millions of animals. Therefore, the MME for these models need to be solved iteratively in practice, commonly through the PCG algorithm. To this end, each iteration requires multiplying the corresponding coefficient matrix with a candidate vector.To illustrate the necessity of a fast genotype matrix multiplication, we give an overview of the matrix operations involved in the ssSNPBLUP approach, proposed by y is the vector of records, b is the vector of nfixed fixed effects, un is the vector of additive genetic effects for the non-genotyped animals, ug is the vector of additive genetic effects for the genotyped animals, and e is the vector of residuals. The matrices X, Wn, and Wg are incidence matrices relating records in y to the corresponding effects. The random effects vector ug can be decomposed into ug = ag + Zg, where g is the vector of SNP effects and ag contains the residual polygenic effects.A standard univariate mixed model for ssGBLUP can be written as:Σ−1 defined asw between 0 and 1 is the proportion of variance not explained by SNP markers, called residual polygenic effects, and n and g denote non-genotyped and genotyped animals respectively. The inverse of Agg can be computed asDue to the assumed covariance structure, the ssSNPBLUP system of equations proposed by s sparse . Here, nAnn, Ang, Agn, Agg) in Σ−1 are sparse and can be multiplied by a vector or a matrix at a relatively low cost by using iteration-on-data techniques  in March 2022. We solved the equation systems associated with the ssSNPBLUP and ssGTABLUP models. The single-step genomic evaluations were based on the same multi-trait animal model and variance components as the current official routine breeding value evaluation described in more detail in ZΛ and 5codes algorithm and the GPU implementation with two alternative solutions: 1) The decompress-on-the-fly approach implemented in Fortran and proposed by dgemm) which is part of all major BLAS libraries. As for the latter, we first needed to inflate the full SNP matrix to double-precision floating-point values and store both the SNP matrix as well as its transpose in memory. We use the BLAS library included in the Intel® Math Kernel Library (MKL). For compilation, we used the Intel® compiler in its version 2021.4.0 and employed compilation options to natively optimize our code to the available hardware. We ran our CPU benchmarks on a single AMD® Milan EPYC 7513 (2.6 GHz) CPU and our GPU implementation on an Nvidia® H100. Since our implementation of the 5codes algorithm did not display considerable scalability advances beyond 20 cores  for the small and medium populations on the GPU (CPU). Unfortunately, the genotype data of the large population in double precision required approx. 2.27 TB of RAM, which could not be met in our hardware setup, hindering us from benchmarking the BLAS library on this dataset. Similarly, the CPU-based original solution for multiplying compressed SNP matrices with ® and AMD® processors (Intel® Xeon Gold 6230 and AMD® Milan EPYC 7513) and our GPU code on three generations of Nvidia® datacenter GPUs . Results displayed in To mitigate the impact of hardware-specific optimizations which might limit the reproducibility of our results, we further test our CPU code on IntelAs for the GPU implementation, our findings suggest that reductions in computing times of approx. 25% (50%) can be achieved when using the recently introduced H100 compared to the A100 (V100). More importantly, the V100 ships with 16 GB or 32 GB of device RAM, limiting the potential problem sizes in our application. Yet, this issue could be mitigated by using multiple GPUs. Since both the transposed and the untransposed matrix are stored on the device, computing times for both multiplications do not differ substantially.® C/C++ Classic Compiler with Intel-specific optimizations, the 5codes algorithm performs slightly better on the more powerful AMD® chip than on the Xeon Gold 6230. We observe that our implementation scales reasonably well to 10 cores, decreasing computing times by at least a factor of 5. However, increasing the number of cores to 20 only yields mild performance improvements and even comes with a penalty in some cases .We solved the equation systems associated with the ssSNPBLUP and ssGTABLUP models with the program hpblup, a PCG-based solver used by the software MiXBLUP 3.1 , which lZΛ and by approx. 95% (76%) for ZΛ was slightly higher in the 5codes algorithm. Yet, both 5codes and the GPU implementation significantly decreased the time for computing Results are displayed in 5codes implementation reduced the time for solving the ssSNPBLUP model from approx. 6.47 h to 4.22 h on the CPU. Similarly, the wall clock time for solving the ssGTABLUP model was reduced from 4.03 h to 3.30 h. Outperforming these results, the GPU approach only required 2.49 h for the ssSNPBLUP model and 1.98 h for the ssGTABLUP model. A similar number of iterations was observed for solving all models, though the 5codes algorithm required 27 iterations less for solving the MME associated with the ssSNPBLUP model, which might be explained by its inherently higher precision.As the genotype matrix multiplication constitutes a significant portion of the time per iteration in the PCG solver, the M by a continuously-scaled matrix Λ which are applicable both on CPUs as well as on modern GPUs. Useful applications include single-step genomic models that are used to compute breeding value estimates when only a subset of animals are genotyped and/or phenotyped. Yet, similar computational operations are employed in other fields of modern genetics. For instance, genome-wide association studies could benefit from a fast genotype matrix multiplication at various computational bottlenecks: the multiplication of the SNP matrix by a phenotype vector is an essential part of the calculation of genotype-phenotype correlations  now constitutes a significant portion of the total computation time. Reducing this contribution holds the potential for additional performance improvements.Notwithstanding these potential improvements, our software can be used in a variety of computational tasks in genomics to reduce computing times.