A hypergraph-based method for large-scale dynamic correlation study at the transcriptomic scale

The biological regulatory system is highly dynamic. Correlations between functionally related genes change over different biological conditions, which are often unobserved in the data. At the gene level, the dynamic correlations result in three-way gene interactions involving a pair of genes that change correlation, and a third gene that reflects the underlying cellular conditions. This type of ternary relation can be quantified by the Liquid Association statistic. Studying these three-way interactions at the gene triplet level have revealed important regulatory mechanisms in the biological system. Currently, due to the extremely large amount of possible combinations of triplets within a high-throughput gene expression dataset, no method is available to examine the ternary relationship at the biological system level and formally address the false discovery issue.

Here we propose a new method, Hypergraph for Dynamic Correlation (HDC), to construct module-level three-way interaction networks. The method is able to present integrative uniform hypergraphs to reflect the global dynamic correlation pattern in the biological system, providing guidance to down-stream gene triplet-level analyses. To validate the method's ability, we conducted two real data experiments using a melanoma RNA-seq dataset from The Cancer Genome Atlas (TCGA) and a yeast cell cycle dataset. The resulting hypergraphs are clearly biologically plausible, and suggest novel relations relevant to the biological conditions in the data.

We believe the new approach provides a valuable alternative method to analyze omics data that can extract higher order structures. The software is at https://github.com/yunchuankong/HypergraphDynamicCorrelation .