Distinct network patterns emerge from Cartesian and XOR epistasis models: a comparative network science analysis

Background: Epistasis, the phenomenon where the effect of one gene (or variant) is masked or modified by one or more other genes, significantly contributes to the phenotypic variance of complex traits. Traditionally, epistasis has been modeled using the Cartesian epistatic model, a multiplicative approach based on standard statistical regression. However, a recent study investigating epistasis in obesity-related traits has identified potential limitations of the Cartesian epistatic model, revealing that it likely only detects a fraction of the genetic interactions occurring in natural systems. In contrast, the exclusive-or (XOR) epistatic model has shown promise in detecting a broader range of epistatic interactions and revealing more biologically relevant functions associated with interacting variants. To investigate whether the XOR epistatic model also forms distinct network structures compared to the Cartesian model, we applied network science to examine genetic interactions underlying body mass index (BMI) in rats (Rattus norvegicus).

Results: Our comparative analysis of XOR and Cartesian epistatic models in rats reveals distinct topological characteristics. The XOR model exhibits enhanced sensitivity to epistatic interactions between the network communities found in the Cartesian epistatic network, facilitating the identification of novel trait-related biological functions via community-based enrichment analysis. Additionally, the XOR network features triangle network motifs, indicative of higher-order epistatic interactions. This research also evaluates the impact of linkage disequilibrium (LD)-based edge pruning on network-based epistasis analysis, finding that LD-based edge pruning may lead to increased network fragmentation, which may hinder the effectiveness of network analysis for the investigation of epistasis. We confirmed through network permutation analysis that most XOR and Cartesian epistatic networks derived from the data display distinct structural properties compared to randomly shuffled networks.

Conclusions: Collectively, these findings highlight the XOR model's ability to uncover meaningful biological associations and higher-order epistasis derived from lower-order network topologies. The introduction of community-based enrichment analysis and motif-based epistatic discovery emphasize network science as a critical approach for advancing epistasis research and understanding complex genetic architectures.