A classification and characterization of two-locus, pure, strict, epistatic models for simulation and detection

Abstract

Background:The statistical genetics phenomenon of epistasis is widely acknowledged to confound disease etiology. In order to evaluate strategies for detecting these complex multi-locus disease associations, simulation studies are required. The development of the GAMETES software for the generation of complex genetic models, has provided the means to randomly generate an architecturally diverse population of epistatic models that are both pure and strict, i.e. all n loci, but no fewer, are predictive of phenotype. Previous theoretical work characterizing complex genetic models has yet to examine pure, strict, epistasis which should be the most challenging to detect. This study addresses three goals: (1) Classify and characterize pure, strict, two-locus epistatic models, (2) Investigate the effect of model 'architecture' on detection difficulty, and (3) Explore how adjusting GAMETES constraints influences diversity in the generated models.Results: In this study we utilized a geometric approach to classify pure, strict, two-locus epistatic models by "shape". In total, 33 unique shape symmetry classes were identified. Using a detection difficulty metric, we found that model shape was consistently a significant predictor of model detection difficulty. Additionally, after categorizing shape classes by the number of edges in their shape projections, we found that this edge number was also significantly predictive of detection difficulty. Analysis of constraints within GAMETES indicated that increasing model population size can expand model class coverage but does little to change the range of observed difficulty metric scores. A variable population prevalence significantly increased the range of observed difficulty metric scores and, for certain constraints, also improved model class coverage. Conclusions:These analyses further our theoretical understanding of epistatic relationships and uncover guidelines for the effective generation of complex models using GAMETES. Specifically, (1) we have characterized 33 shape classes by edge number, detection difficulty, and observed frequency (2) our results support the claim that model architecture directly influences detection difficulty, and (3) we found that GAMETES will generate a maximally diverse set of models with a variable population prevalence and a larger model population size. However, a model population size as small as 1,000 is likely to be sufficient.

Epistatic interaction between common AGT G(− 6)A (rs5051) and AGTR1 A1166C (rs5186) variants contributes to variation in kidney size at birth

“…This observation highlights the importance of considering gene-gene interaction in discovering the genetic architecture of quantitative traits, even when the loci do not show significant single locus effects (i.e. when the model is purely epistatic Urbanowicz et al, 2014). Using simulated regulatory networks, Gjuvsland et al (2007) have shown that statistical epistasis is generated by functionally-dependent genes and the amount of genetic variance explained by epistatic interaction depends on the sign of the feedback.…”

Leveraging putative enhancer-promoter interactions to investigate two-way epistasis in Type 2 Diabetes GWAS

“… 12 – 13 The latter is certainly a reasonable approach; however it will miss potential interactions which involve SNPs with no main effects (i.e. it will miss what is referred to as ‘pure and strict epistasis’ 14 ).…”

Identification of SNP-SNP Interaction Using Entropy-Based Multifactor Dimensionality Reduction in Case-Control Studies

“…Two of the 2-locus models are the models with marginal effects. Junghyun Namkung et al developed Models 1 (Table III) and 2 (Table IV) [14] by varying the strength of genetic effects while fixing the interaction structure, the minor allele frequency (MAF) and prevalence. Two of the 3-locus models are called XOR model [15] (Table V) and ZZ model [16], [17] (Table VI), respectively.…”