# Exhaustive Variant Interaction Analysis Using Multifactor Dimensionality Reduction
## 3 Results
### Functional Interpretation of the T2D-Associated Pairs  
To investigate the connections between the signals detected by the MDR model and the disease, we first annotated the variants present in each pair. The 104 pairs of variants statistically associated with type 2 diabetes (T2D) obtained by applying our method contain 125 unique variants. Importantly, after annotating the 125 loci with GWAS meta-analyses and gene expression [23; 36; 37; 38; 39; 40; 41], we observed that a large number of variants were already known when compared with a control set. More specifically, 93% (4.65-fold) of the variants are in LD with an already known T2D-related signal. Notably, 6% of the variants are in LD with an islet eQTL, 1% cASE, and 50% GTEx eQTL (Figure 6). While the replication of these signals is a reflection of the additive effect of the variants in the disease, the 7% of novel signals remain unexplained under a non-interaction model.  
In addition, to understand the possible biological mechanisms underlying our findings, we conducted a gene functional enrichment analysis. The list of genes obtained for each pair from these annotations was used for a gene functional enrichment analysis [43]. Among the results obtained from the analysis, we found to be of particular interest the one derived from the pair composed of rs6450946 (chr5:33120048) and rs1219643 (chr10:123348355), which involves _FGFR2_ signaling. Importantly, _FGFR2_ is known to upregulate adiposity [45]. Decreased expression of this gene might be a compensatory response to enhanced adiposity, thus suggesting its possible relevance as a novel therapeutic approach for obesity [46], and its overexpression has been suggested to be linked with embryo development and infertility  
Figure 6: Box plots showing the percentage of already known variants in the interacting pairs in contrast with a control set in (**A**) general, (**B**) GWAS significant variants [23; 37; 38; 39], (**C**) 2 h glucose and fasting-glucose significant variants [36], (**D**) insulin significant variants [36], (**E**) pancreatic islet expression quantitative trait loci significant signals [40], (**F**) islet combined allelic specific expression significant signals [40], and (**G**) GTEx expression quantitative trait loci significant signals [41]. The red dots represent the percentage of variants in each pairwise interaction with a known annotation. The blue and grayscale box plots correspond to the distribution of the percentage of annotated variants in the control set.  
in maternal diabetes [47]. In addition, the pair composed of rs2007/76585 (chr1:162626640) and rs72806227 (chr5:159084262) is connected with the regulation of the hepatic stellate cell proliferation pathway. Interestingly, diabetic hepatic fibrosis is a progressive liver disease and a chronic complication of diabetes mellitus and is known to be mainly caused by the activation of quiescent hepatic stellate cells (HSCs) by high glucose stimulation [48]. The activation of these cells is known to be promoted by _TSC22D4_[49], which is a gene that acts as a critical controller of diabetic hyperglycemia [50] and has elevated levels in patients with T2D with non-alcoholic fatty liver disease or steatohepatitis. In summary, these results suggest that the associations found between the interactions and type 2 diabetes can be mediated by the connection between variants with gene expression and their combined effects on gene pathways.