The cohesin complex has multiple essential roles during cell division in mitosis and meiosis, genome organisation, DNA damage repair, and gene expression 1 . Mutations in genes that encode members of the cohesin complex, or its regulators, cause developmental diseases known as the 'cohesinopathies' when present in the germline 2 ; or contribute to the development of cancer in somatic cells [3] [4] [5] .
Remarkably, cohesin mutations are almost always heterozygous, and result in depletion of the amount of functional cohesin without eliminating it altogether. Complete loss of cohesin is not tolerated in healthy individuals 2 . Thus, cohesin is haploinsufficient such that normal tissue development and homeostasis requires that the concentrations of cohesin and its regulatory factors remain tightly regulated.
The human mitotic cohesin ring contains four integral subunits: two structural maintenance proteins (SMC1A, SMC3), one stromalin HEAT-repeat domain subunit (STAG1 or STAG2), and one kleisin subunit (RAD21) 6 . Mutation of STAG2 has been linked to at least four tumour types (e.g. Ewing sarcoma, glioblastoma and melanoma 7 , and bladder carcinomas) 4 . Strikingly, mutations in cohesin components are especially prevalent in acute myeloid leukaemia [8] [9] [10] .
In meiotic cohesin, SMC1A is replaced by SMC1B; STAG1/2 by STAG3; and RAD21 by REC8 or RAD21L1 1 . Mutations in meiotic cohesin subunits are associated with infertility in men 11 , chromosome segregation errors and Primary Ovarian Insufficiency in women 12 .
Cohesin is loaded onto DNA by the SCC2/SCC4 complex (encoded by the NIPBL and MAU2 genes, respectively) 1 . Mutations in the cohesin loading factor NIPBL are associated with >65% cases of Cornelia de Lange Syndrome (CdLS). Remarkably, features associated with CdLS are observed with less than 30% depletion in NIPBL protein levels 13 .
The release of cohesin from DNA is achieved by WAPL, which opens up the interface connecting the SMC3 and RAD21 subunits. The PDS5A/PDS5B cohesin associated subunits affect this process by contacting cohesin to either maintain (with STAG1 and STAG2) or remove (with WAPL) the ring from DNA 1 .
Spatial organization and compaction of chromosomes in the nucleus involves non-random folding of DNA on different scales. The genome is segregated into active A compartments and inactive B compartments 14 , inside which further organisation occurs into topologically associating domains (TADs) interspersed with genomic regions with fewer interactions 14 . Cohesin participates in genome organisation by mediating 'loop extrusion' of DNA to form loops that anchor TAD boundaries. At TAD boundaries, cohesin colocalizes with the CCCTC binding factor (CTCF) to form chromatin loops between convergent CTCF binding sites. Fine-scale genomic interactions include chromatin loops that mediate promoter-enhancer contacts. Notably, the time-and tissue-specific formation of the fine-scale loops also requires cohesin.
The spatial organization of the genome is particularly dynamic and susceptible to disruption during development. For example, changes to TAD boundaries are associated with developmental disorders 15 . Furthermore, disruption of TAD boundaries by cohesin knockdown can lead to ectopic enhancer-promoter interactions that result in changes in gene expression 16 . Rewiring of the patterns of course and fine-scale chromatin interactions also contributes to cancer development 17, 18 , including the generation of oncogenic chromosomal translocations 19, 20 .
Disease-associated GWAS variants in non-coding DNA likely act through spatially organized hubs of regulatory control elements, each component of which contributes a small amount to the observed phenotype(s), as predicted by the omnigenic hypothesis 21, 22 . Non-coding mutations at cohesin and cohesin-associated factors were found by genome wide association studies (GWAS-attributed variants) to track with multiple phenotypes 23 . However, the impact of genetic variants located within cohesin and its associated genes has not yet been investigated with respect to phenotype development.
We hypothesised that cohesin-associated pathologies can be affected by subtle, combinatorial changes in the regulation of cohesin genes caused by common genetic variants within control elements. Here, we link the 3D structure of the genome with eQTL data to determine if GWAS variants attributed to cohesin genes affect their transcription. We test cohesin gene-associated GWAS variants for regulatory connections beyond the cohesin genes (gene enrichment and regulatory hubs). We also identify all variants within each gene locus that had a previously determined cis-eQTL (GTEx Catalog) to the cohesin gene (eQTL-attributed variant list). As with the GWAS variants, we tested these variants for the presence of spatial-regulatory relationships involving genes outside of the locus. Only a few of these eQTL-attributed variants are currently implicated in disease pathways, but their regulatory relationships with cohesin suggest that they may be significant for cohesinopathy disorders.
Results 140 genetic variants with regulatory potential are associated with cohesin loci Mitotic cohesin genes (SMC1A, SMC3, STAG1, STAG2, and RAD21), meiotic cohesin genes (SMC1B, STAG3, REC8, and RAD21L1), cohesin support genes (WAPL, NIPBL, PDS5A, PDS5B, and MAU2) and CTCF were investigated to determine if they contain non-coding genetic variants (SNPs) that make contact in 3D with genes and therefore could directly affect gene expression (GWAS-attributed and eQTL-attributed; Table 1, Table S1 ).
A total of 106 GWAS-attributed genetic variants associated with disease were identified (methods) that mapped to a cohesin gene (49 GWAS; 50 SNPs) or cohesin-associated (49 GWAS; 56 SNPs) gene (Table S1 ). Twelve SNPs (blue , Table S1 ) are not listed in the current GTEx SNP dictionary (GTEx v8), while fourteen SNPs have virtually no variation in the GTEx per-tissue analysis (i.e. minor allele frequency [MAF] < 0.05; green, Table S1 ) and so were discarded. 80 SNPs passed all filters and were subsequently analysed using CoDeS3D 21 (GWAS-attributed list; Table 1 ).
Within the GTEx catalogue, 187 eQTL-attributed variants associate with regulation of the cohesin gene set (Table S1 ). These variants associate with modified expression levels of cohesin genes in otherwise healthy individuals. Fifty-five of these variants had a MAF<0.05 (green , Table S1 ) and were filtered out of the eQTL-attributed set prior to CoDeS3D analysis (132 variants passed MAF filter; eQTL-attributed; Table 1 ). Only three variants were shared between the GWAS-attributed and eQTLattributed variant lists, resulting in a total of 290 cohesin-associated variants (GWAS-and eQTL-attributed combined; Table 1 ), but only 209 variants pass all filters (GWAS-and eQTL-attributed combined; black, Table S1 ).
CoDeS3D integrates data on the 3-dimensional organisation of the genome (captured by Hi-C) and transcriptome (eQTL) associations across multiple tissue types (Table S2 and S3). We used the CoDeS3D algorithm to assign the 209 variants to hubs of regulatory/functional impacts by examining their potential to regulate other genes. Of the 209 variants, four had zero significant eQTLs, leaving 205 variants with significant eQTLs (128 eQTL-attributed, 80 GWAS-attributed, and 3 overlaps; Table  S2 and S3). However, many of the 205 variants were not attributed the GWAS-or eQTL-attributed cohesin gene in the locus. Of the 205 variants with eQTLs, 106/187 (56.7%) eQTL-attributed variants and 37/106 (34.9%) GWAS-attributed variants had a physical (Hi-C detected) connection and significant eQTL with their attributed cohesin gene (140 total, 3 overlaps; Table 1 ).
Strikingly, most of the 106 variants attributed by GWAS studies to cohesin genes were not confirmed by spatial connection, with only 34% being cis-eQTLs for the attributed cohesin gene (37 of 106, 34.9%). After the CoDeS3D analysis, six of the cohesin genes have no GWAS-attributed SNPs with a regulatory connection (STAG2, NIPBL, CTCF, SMC3, REC8, and RAD21-AS1). Therefore, the majority of GWAS variants tested in proximity to cohesin loci have regulatory effects elsewhere in the genome. Remarkably, despite five SNPs being attributed to NIPBL by GWAS, none of these were attributed to regulation of NIPBL by our spatial eQTL analysis. Of the cohesin or cohesin-associated genes with any GWAS-attributed variants with cis-eQTLS (RAD21, RAD21L1, SMC1A, SMC1B, STAG1, STAG3, MAU2, PDS5A, PDS5B, and WAPL), only the STAG1, MAU2, and PDS5B loci contain more than two variants with confirmed cis-eQTLs. Therefore, even those loci with confirmed variant-gene GWAS attributions have very few variants with evidence of cis-eQTLs.
To further characterize the potential for the 209 cohesin-associated variants to alter gene regulation, we analysed histone marks, DNAse accessibility, and protein binding motifs (Haploreg v 4.1) at each location (Table S4) 24 . Most variants reside within accessible chromatin (DNAse: 61.3%) and almost all (93.1%) have at least one of three histone marks that are consistent with putative regulatory activity (promoter, 82.8%; enhancer, 45.1%; protein binding sites, 86.8%). Intriguingly, Haploreg motif prediction identified 16 of the 209 variants (7 different loci: MAU2, PDS5B, REC8, SMC1B, STAG3, RAD21L1, STAG1) as residing within protein binding domains associated with cohesin-related DNA interactions (i.e. RAD21, SMC3, and CTCF). Therefore, most of the variants like in regions associated with chromatin marks that highlight putative regulatory capabilities.
CoDeS3D predicted 140 out of 209 variants to have significant regulatory activity. We compared this to alternative functional variant prediction methods. The DeepSEA algorithm, which predicts the chromatin effects of sequence alterations by analysing the epigenetic state of a sequence, identified 28 of 209 the variants as having functional significance (<0.05, Table S5 ). PredictSNP2, which estimates noncoding variant classification (deleterious or neutral) from five separate prediction tools (CADD, DANN, FAT, FUN, GWAVA tools), identified 9 of 209 variants as deleterious (Table S6) . Therefore, only 31/209 variants have putative functional significance predicted by these tools (28 DeepSEA, 9 PredictSNP, 6 overlaps). Therefore, these 31 variants have support from multiple methods, suggesting a potential for higher regulatory effects, and that the contrast with the Haploreg chromatin marks and GTEx measured eQTLs possibly indicates a heavy weighting against false positives in these prediction methods.
In summary, GWAS-attributed SNPs are enriched for chromatin marks (regulatory potential). However, fewer than half the SNPs in proximity to the cohesin and cohesin-associated genes physically connected with the cohesin genes they are predicted to regulate, suggesting that cohesin genes are not the direct targets of these regulatory variants.
Pathway enrichment implicates coordinated regulation of cohesin with essential cell cycle genes CoDeS3D identified 140 variants as being physically connected to, and associated with the expression levels of 310 genes (243 genes from eQTL-attributed variants, 141 from GWAS-attributed variants, and 74 overlap) across 6,795 significant tissue-specific regulatory connections (FDR p<0.05). Physical connections comprised 6,570 fine-scale connections (cis, <1Mb from the variant), 42 coarsescale connections (trans-intrachromosomal, >1Mb), and 183 connections on a different chromosome (trans-interchromosomal) (Fig 1; Tables S2, S3). Of note, there is one cohesin-tocohesin regulatory connection: rs111444407, a GWAS-associated variant (bipolar disorder) located within the MAU2 locus has a significant trans-interchromosomal eQTL with REC8. The gene overlaps between the GWAS-and eQTL-attributed analyses are also intriguing. For example, variants in the GWAS-attributed and eQTL-attributed lists, each from a different chromosomal location (REC8 and PDS5B), modify TCF7L1 expression. As TCF7L1 is part of the Wnt pathway and is highly expressed in ovaries in the GTEx catalogue, it is notable that this gene is regulated from variants in the REC8 locus (meiosis-specific cohesin). Their co-regulatory relationships exemplify the systems of genomeregulatory hubs, with a total 74 genes overlapping the GWAS-and eQTL-attributed analyses.
The 31 significant variants highlighted by the DeepSEA and PredictSNP2 analyses functionally connected to 107 (34.5%) of the genes identified by CoDeS3D. Thus, while DeepSEA and PredictSNP2 assigned functionality to just 31/205 SNPs (15.1%), these variants represent 34.5% of the CoDeS3Dpredicted modulatory connections. Therefore, DeepSEA and PredictSNP2 successfully selected for variants with highly enriched regulatory functions.
We used g:Profiler to assess the functional enrichment of the GWAS-and eQTL-attributed genes ( Table S7 ). The 310 genes are enriched for pathways that support cohesin function, as we currently understand it, within the nucleus. For example, functional enrichment in sister chromatid gene ontology categories includes five non-cohesin genes from our analysis: CTNNB1, PPP2R1A, CHMP4A, CUL3, and DIS3L2. Moreover, cohesin's meiosis-specific role (SMC1B, STAG3, REC8) is enriched by two trans connections revealing regulation of meiosis-related genes (ITPR2, PPP2R1A; KEGG pathway hsa04114). Collectively, these results suggest that expression of cohesin genes is coordinated with other genes that are involved in cell cycle control.
Meiosis-specific cohesin genes are functionally connected to KIF6 and a germ cell pathway There are 108 genes functionally connected to variants within the meiosis-specific cohesin loci SMC1B, STAG3, REC8, and RAD21L1 (Table S8a) . We identified 14 significant enrichment terms using g:Profiler (Table S8b) , including the gene ontology "male germ cell nucleus" pathway. The gene ontology "male germ cell nucleus" pathway contains KIF6, STAG3, and REC8 (trans-interchromosomal connection from STAG3 locus to KIF6). Within GTEx, KIF6 is highly expressed in brain and testis. The KIF6 gene region was previously identified as significantly associated with a GWAS of hypospadias, a birth defect presenting with a urethral opening located on the ventral side of the penis instead of at the tip of the glans. Of particular relevance to the cohesinopathies, in which affected individuals present with cognitive defects, a mutation in human KIF6 caused neurodevelopmental defects and intellectual disability 25 . Variation in KIF6 expression has been associated with epilepsy 26 , another notable cohesinopathy phenotype 27 . It has also been proposed that KIF6 is a conserved regulator of neurological development 25 . Previous findings of an association between KIF6 and heart disease are not supported by GTEx (KIF6 is lowly expressed in GTEx heart tissue) and KIF6 knockout mice have no heart phenotype 28 , suggesting that the heart-associated KIF6 variants might somehow affect the expression or function of other genes.
We also identified an enrichment for E2F7 transcription factor binding sites within our genes ( Table  S8b ). The E2F7 transcription factor modulates embryonic development and cell cycle 29, 30 , with a role in cancer development 31 . Of note, the E2F7 gene is loss-of-function intolerant (pLI=.993), consistent with its crucial role in the cell cycle and development.
Collectively, our results suggest that the 301 genes are enriched for cell cycle-regulated genes, including E2F targets, and that these genes might be indirect targets of cancer drug treatments modifying E2F7 transcription factor activity.
The cohesin gene regulatory network is intolerant to loss-of-function mutations A subset of human genes, whose activity is crucial to survival, are intolerant to loss-of-function (LoFintolerant) mutations 32 . The gnomAD catalog lists 19,704 genes: 3,063 LoF-intolerant, 16,134 LoFtolerant, and 507 undetermined (15.5% LoF-intolerance, defined as pLI ≥ 0.9) 32 . All cohesin and cohesin-associated genes (except the meiosis-only RAD21L1, SMC1B, STAG3, and REC8) are LoFintolerant (Table 2) .
We hypothesized that genes functionally connecting to variants in cohesin genes would also be enriched for loss-of-function intolerance. Consistent with our hypothesis, 79 of the 310 genes (25.4%) we identified are LoF-intolerant (185 are LoF tolerant and 46 have undetermined pLI; Table  S9 ). Stratification of the eQTL genes based on the distance between the variant and gene (cis versus trans-acting eQTL gene lists) identified a marked increase in LoF-intolerance for genes regulated by trans-acting eQTLs (Fig 2; Fig S1) .This was especially pronounced for regulatory interactions that occurred between chromosomes (Fig 2; Fig S1) . There was a significant correlation between distance and pLI on the same chromosome (r=-0.03, p<0.05).
As the cohesin genes are intolerant to even small perturbations in gene expression, we hypothesized that the LoF-intolerant genes that were regulated by elements within the cohesin genes would similarly only be tolerant to small allelic fold changes in gene expression. Therefore, we tested for a correlation between pLI and the allelic fold change (log2 aFC) associated with the eQTL. We observed that pLI is significantly correlated with aFC (r=-0.07, p<0.01; Fig 3) . Ignoring the direction of the change in expression, by using the absolute value of log2 aFC, we identified an even stronger negative correlation between pLI and |aFC| (r=-0.31, p<0.01; Fig 4) . Collectively, these results are consistent with the hypothesis that long distance (especially inter-chromosomal) regulatory connections exhibit greater tissue specificity and disease associations 22,33 because they are enriched for LoF-intolerant gene sets. Thus, the inter-chromosomal regulatory connections potentially highlight novel disease pathways associated with the known cohesinopathies.
Pathway analysis identifies cohesin gene connections with extracellular matrix production and the proteasome We hypothesized that genes connected to regulatory variants within the cohesin loci might be contributing to disease-related phenotypes. A g:Profiler TRANSFAC analysis identified significant enrichment for target sequences for the EGR1 transcription factor (Table S7) . EGR1 transcription is regulated by stress and growth factor pathways; its binding to DNA is modulated by redox state, and its transcriptional targets include genes involved in extracellular matrix production 34 . g:Profiler enrichment also identified 9 genes as part of the ubiquitin mediated proteolysis pathway (BIRC3, BIRC6, CUL2, UBE2F, UBE2K, UBE4B, UBR5, CUL3, XIAP; Tables S7 [red] and S10). The proteasome pathway tags unwanted proteins to be degraded and defects in proteolysis have a causal role in a variety of cancers. Notably, 8 of the 9 (88.9%) genes identified in the Ubiquitin-mediated proteolysis pathway are LoF-intolerant.
We hypothesized that the 310 genes we identified would have pharmacokinetic interactions with cancer treatments. Notably, we identified CYP3A5 as being regulated by a cis interaction with a variant 441,888 bp away (intronic, CNPY4). CYP3A5 encodes a protein within the cytochrome P450 family. Defects in P450 are known to alter cancer treatment outcomes (drug metabolism, KEGG hsa00982). Additionally, we identified a g:Profiler enrichment for the E2F7 transcription factor within our eGenes. E2F7 is up-regulated in response to treatment with doxorubicin or etoposide, topoisomerase 2 blockers 31 . Indeed, many of the 310 genes from the CoDeS3D analysis are targeted by drugs (Table S11) . By contrast, for the cohesin genes, the drug-gene interaction database only lists known drug interactions for STAG2 and STAG3 35 . Notably, consistent with our earlier observations, the drug-gene targets we identified include two genes targeted by topoisomerase blockers (e.g. PAPOLA, and XIAP) 35 , both of which are LoF-intolerant genes.
Through the use of the "Contextualize Developmental SNPs using 3D Information" (CoDeS3D) algorithm 21 , we have leveraged physical proximity (Hi-C) and gene regulatory changes (eQTLs) to reveal how variation in putative enhancers can alter the regulation of cohesin genes and modifier genes. Our analysis has identified 140 eQTLs that link 310 genes associated with the mitotic cohesin ring genes (SMC1A, SMC3, STAG1, STAG2, and RAD21/RAD21-AS), meiosis-specific cohesin ring genes (SMC1B, STAG3, REC8, and RAD21L1), cohesin-associated support proteins (WAPL, NIPBL, PDS5A, PDS5B, and MAU2) and CTCF. Collectively, these results form an atlas of functional connections from cohesin genes to proximal and distal genes, some of which reside on different chromosomes to the regulatory elements. These results agrees with previous findings that spatial eQTLs mark hubs of activity across a multi-morbidity atlas 21 .
Only 35% of variant-gene mappings in the GWAS catalogue were supported by spatial cis-eQTLs. Therefore, although several GWAS-associated disease SNPs have been linked with cohesin, only a minority have supporting evidence that these variants actually regulate the cohesin genes. As such, our results call into question the validity of many of the previous associations between non-coding genetic variants and the cohesin genes that have been made in the GWAS catalogue.
Previous reports have suggested that cis-eQTL gene sets are depleted of LoF-intolerance genes when compared to similarly sized sets of non-eQTL genes 36 . Similarly, our findings show that the 310 genes regulated by variants in cohesin loci are also enriched for LoF-intolerant genes is notable. The apparent bias in existing studies can be explained by eQTL studies being predominantly focused on nearby (cis) variant-gene transcriptional connections and Hi-C studies focusing on local changes in TAD structure, due to technical limitations in the current analysis pipelines.
We revealed that the greater the distance separating the eQTL and target gene, the more likely the target gene was to be LoF-intolerant (i.e. over 30% of trans-interchromosomal interactions involved LoF-intolerant genes). This finding is consistent with studies that show that long distance connections exhibit greater disease-and tissue-specificity 22, 33, 37 . The demonstration that the cohesion genes are also LoF-intolerant agrees with their recognised haploinsufficiency in human developmental disease 2, 13 . Notably, the genes that were enriched within pathways of pathological importance (e.g. 8 of the 9 genes in the ubiquitin-mediated proteolysis pathway gene set) were more likely to be LoF-intolerant. This is consistent with previous findings that eQTL-identified genes are enriched for genome-wide disease heritability, and the subset of eQTL genes with LoFintolerance are even larger enrichments for genome-wide disease heritability 38 .
The CoDeS3D method identified eQTL links between cohesin genes and other loci not related to cohesin. Two pathways emerged from this analysis. Firstly, spatial eQTL connections with cohesin genes identified an enrichment for genes that are regulated by zinc finger transcription factors including EGR1 and ZNF880. EGR1 positively regulates extracellular matrix (ECM) production. Interestingly, we recently observed widespread dysregulation of extracellular matrix genes upon deletion of cohesin genes in leukaemia cell lines 39 . This supports the idea that regulation of the cohesin complex is tightly associated with ECM production. Additional support for this is derived from the observation that cohesin subunit SMC3 exists in the form of an extracellular chondroitin sulfate proteoglycan known as bamacan 40 . Additionally, in asthma, SMC3 upregulation significantly affected ECM components 41 . The ECM facet of cohesin biology is relatively under-explored and is worthy of further investigation. Secondly, spatial eQTL connections with cohesin genes identified an enrichment for genes that encode effectors of the proteasome pathway. The stability of many cohesin proteins are regulated by the proteasome pathway 1,42,43 , but aside from this, genetic interactions between cohesin genes and proteasome pathway genes remain unexplored.
In conclusion, many studies of mutations focus on the impact of coding-region variation, relying on natural knockouts (especially missense and loss of function variants) to identify gene function. Our analysis highlights what those studies might be missing: sets of co-ordinated genes important to disease but largely intolerant to LoF mutation in healthy individuals. We identified a novel set of genes which are regulated by elements within the cohesin genes. We found that many of the pathways and transcription factor binding sites enriched within these genes were relevant to disease pathways relevant to development and cancer. Moreover, drug-gene interactions further reinforce the importance of these connections to cancer drug treatments and in particular topoisomerasetargeting drugs. As such, our results support recent reports of the importance of long-distance regulation as a key driver of phenotype development 33 . Methods A large number of GWAS studies have mapped phenotypic variation to cohesin ring gene loci
We searched the GWAS catalogue for SNPs mapped or attributed to mitotic cohesin ring genes (SMC1A, SMC3, STAG1, STAG2, and RAD21/RAD21-AS), meiosis-specific cohesin ring genes (SMC1B, STAG3, REC8, and RAD21L1), cohesin-associated support proteins (WAPL, NIPBL, PDS5A, PDS5B, and MAU2), and CTCF from GWAS studies covering a large assortment of altered phenotypes and pathologies across most tissues in the body (GWAS-attributed).
Genomic positions of SNPs were obtained from dbSNP for human reference hg38.
Beyond variants with association to disease, we searched the GTEx catalogue for cis-regulatory variants (variants within 1Mb) that modify the expression of either cohesin ring genes (SMC1A, SMC1B, SMC3, STAG1, STAG2, STAG3, RAD21, REC8, and RAD21L1), cohesin support genes (WAPL, NIPBL, PDS5A, PDS5B, and MAU2), or CTCF in one or more of 44 tissues across the human body (eQTL-attributed). Unlike GWAS variants, these variants have no inherent association to a phenotype (except the overlaps), as GTEx contains individuals that were relatively healthy prior to mortality. Thus, these variants explain variation in gene expression in a normal, mostly older cohort.
Genomic positions of SNPs were obtained from dbSNP for human reference hg38.
For all GWAS-attributed and eQTL-attributed variants, spatial regulatory connections were identified through genes whose transcript levels depend on the identity of the SNP through both spatial interaction (Hi-C data) plus expression data (expression Quantitative Trail Locus [eQTL]; GTEx v8 45 ) using the CoDeS3D algorithm (https://github.com/Genome3d/codes3d-v1) 21, 46 . Spatial-eQTL association p-values were adjusted using the Benjamini-Hochberg procedure, and associations with adjusted p-values < 0.05 were deemed spatial eQTL-eGene pairs. Variants not found in the GTEx catalogue or variants with a minor allele frequency below 5% were filtered out due to the sample size of GTEx at each tissue.
To identify SNP locations in the Hi-C data, reference libraries of all possible Hi-C fragment locations were identified through digital digestion of the hg38 human reference genome with the same restriction enzyme employed in preparing the Hi-C libraries (i.e. MboI, HindIII). Digestion files contained all possible fragments, from which a SNP library was created, containing all genome fragments containing a SNP. Next, all SNP-containing fragments were queried against the Hi-C databases to find distal fragments of DNA which spatially connect to the SNP-fragment. If the distal fragment contained the coding region of a gene, a SNP-gene spatial connection was confirmed. There was no binning or padding around restriction fragments to obtain gene overlap. To limit technological challenges, gene transcripts for both the spatial and eQTL analyses used the GENCODE transcript model. Spatial connections were identified from previously generated Hi-C libraries of various origins (Supp Table 12 ): 1) Cell lines GM12878, HMEC, HUVEC, IMR90, K562, KBM7, HELA, NHEK, and hESC (GEO accession numbers GSE63525, GSE43070, and GSE35156); 2) tissue-specific data from ENCODE sourced from the adrenal gland, bladder, dorsolateral prefrontal cortex, hippocampus, lung, ovary, pancreas, psoas muscle, right ventricle, small bowel, and spleen (GSE87112); and 3) Tissues of neural origin from the Cortical and Germinal plate neurons (GSE77565), Cerebellar astrocytes, Brain vascular pericytes, Brain microvascular endothelial cells, SK-N-MC, and Spinal cord astrocytes (GSE105194, GSE105513, GSE105544, GSE105914, GSE105957), and Neuronal progenitor cells (GSE52457).
The human transcriptome consists of genes with varying levels of redundancy and critical function, resulting in some genes being intolerant to loss-of-function (LoF-intolerant) mutation. This subset of the human transcriptome are posited to also be more intolerant to regulatory perturbation. The gnomAD catalog 32 lists 19,704 genes and their likelihood of being intolerant to loss-of-function mutations (pLI), resulting in 3,063 LoF-intolerant, 16,134 LoF-tolerant, and 507 undetermined (15.5% LoF-intolerance, defined as pLI ≥ 0.9) 32 . We tested all cohesin, cohesin-associated genes, and those from our analysis (GWAS-and eQTL-attributed) for LoF-intolerance, comparing our cis and transacting eQTL gene lists for enrichment for LoF-intolerance. As pLI is bimodal and non-normally distributed, we tested both pLI raw values as well as pLI grouping (tolerant vs intolerant) for correlation between eQTL effect size (log2 allelic fold change, aFC) and intolerance to disruption (pLI). We considered both aFC and its absolute value (direction of effect ignored), as it has been suggested that the eQTL effect direction is determined by how you define the minor allele within the population, not the actual molecular impact of the eQTL on the cohesin connection. This analysis highlights the significance of long-distance gene regulation on otherwise mutationally-constrained (LoF-intolerant) genes.
All genes from the GWAS-attributed and eQTL-attributed analyses were then annotated for significant biological and functional enrichment using g:Profiler 47 , which includes the Kyoto Encyclopedia of Genes and Genomes (KEGG) Pathway Database (https://www.kegg.jp/kegg/pathway.html) for pathways and TRANSFAC for transcription factor binding enrichment. Finally, we identified drugs that target the genes and related mechanisms through the Drug Gene Interaction database (DGIdb) 35 .
To predict the most phenotypically causal variants within the variant set, we compared variants from the CoDeS3D analysis with several tools which leverage deep learning-based algorithmic frameworks to classify functional relevance from DNA markers including identified chromatin marks (enhancer marks, etc). We used DeepSEA 48 to predict the chromatin effects of variants to prioritize regulatory variants and PredictSNP2 49 to summarise estimates of noncoding variants for classification (deleterious or neutral). DeepSEA predicts the chromatin effects of sequence alterations by analysing the epigenetic state of a sequence (transcription factors binding, DNase I sensitivities, and histone marks) across multiple cell types. PredictSNP2 predictions are a consensus score from across five separate prediction tools for variant prioritization: CADD 1. Tables   Table 1 
The eQTL-attributed variant list consists of 187 variants, but after filtering results in 106 variants with significant spatial eQTLs. The GWAS-attributed variant list consists of 106 variants, but after filtering results in 37 variants with significant spatial eQTLs. Overall, the 290 attributed variants results in 140 variants with significant spatial eQTLs. Table 2 . pLI of cohesin genes shows largely mutation intolerance
The main set of genes comprising cohesin and cohesin-support are all loss-of-function intolerant (pLI > 0.9). However, the subset of cohesin genes specific to only meiosis are not loss-of-function intolerant.
The eQTL-attributed variant list consists of 187 variants, but after filtering results in 106 variants with significant spatial eQTLs. The GWAS-attributed variant list consists of 106 variants, but after filtering results in 37 variants with significant spatial eQTLs. Overall, the 290 attributed variants results in 140 variants with significant spatial eQTLs. Red: variants overlapping each set; Green: variants filtered from CoDeS3D for minor allele frequency (MAF) < 0.05; Blue: variants not in the GTEx variant dictionary (no variant in GTEx).
CoDeS3D scans the GWAS-attributed variant list (106 variants) for variants with physical proximity to genes that is supported by allele-specific gene expression changes (eQTLs). This analysis found 2188 variant-gene-tissues connections, involving 37 GWAS-attributed variants.
CoDeS3D scans the eQTL-attributed variant list (187 variants) for variants with physical proximity to genes that is supported by allele-specific gene expression changes (eQTLs). This analysis found 4607 variant-gene-tissues connections, involving 106 eQTL-attributed variants. We analysed the 209 genetic variants we identified for patterns of histone marks, DNAse accessibility, and protein binding motifs in Haploreg v 4.1. Most of the variants have marks of accessible chromatin (DNAse: 61.3%). In addition, almost all of the variants (93.1%) have at least one of the three: Promoter histone marks (82.8%), Enhancer histone marks (45.1%), proteins binding site (86.8%). Additionally, 16 of the variants modify protein binding or motif predictions in RAD21 (12), SMC3 (4), and/or CTCF (10). Green: protein or motif lists including a cohesin gene.
Supplementary Table 5 . DeepSEA estimated effect of the cis-associated and GWASassociated variants DeepSEA predicts the chromatin effects of sequence alterations by analysing the epigenetic state of a sequence (transcription factors binding, DNase I sensitivities, and histone marks) across multiple cell types. This results in 28 variants identified as functionally significant.