Analysis of higher order interactions quantifies co-ordination in the epigenome and reveals novel biological relationships in Kabuki syndrome

Complex direct and indirect relationships between multiple variables are a characteristic of all natural systems and are defined as higher order interactions (HOIs). Traditional differential and network analyses fail to account for the richness of omic datasets and miss HOIs. We investigated genome-wide peripheral blood DNA methylation data from Kabuki syndrome type 1 (KS1) and control individuals, identified 2,002 differentially methylated points (DMPs), and inferred 17 differentially methylated regions, which represent only 189 DMPs. We followed these results with quantification of HOIs by applying hypergraph network models on all the CpGs in the two datasets and revealed differences in co-ordination of the DMPs along with lower entropy and higher co-ordination of the peripheral epigenome in KS1 implying reduced network complexity. We demonstrate that the hypergraph approach captures substantially more information, enables factoring trans-relationships, and identifies biologically relevant pathways that escape the standard analyses. These findings construct the basis of a suitable model that is not computationally intensive for the analysis of the organisation of the epigenome in rare diseases. This approach can be applied to other types of omic datasets, and to other fields of science and medicine to investigate mechanism in big data.