Empirical Bayes spline model learns multi-way genomic interactions from single cell 3D genome data

A number of foundational analysis methods have emerged for single cell chromatin conformation (scHi-C) datasets capturing 3D organizations of genomes at the single cell resolution; however, these scHi-C datasets are currently under-utilized. The canonical uses of the existing scHi-C data encompass, beyond standard cell type identification through clustering and trajectory analysis, inference of chromosomal structures such as topologically associated domains, A/B compartments, and pairwise interactions. However, multi-way interactions, e.g., looping among multiple genomic elements such as multiple enhancers of a gene, are entirely overlooked. We introduce ELECT, an empirical Bayes modelling framework to Extract muLti-way gEnomiC inTeractions by leveraging scHi-C data. ELECT builds on a dirichlet-multinomial spline model, incorporates well-known genomic distance bias of the chromatin conformation capture data, and yields multi-way interaction scores by leveraging corresponding pairwise interactions across cells of the same type. The multinomial-poisson transformation enables parameter estimation and inference for ELECT in a computationally feasible way for both low and high resolution single cell chromatin conformation data. ELECT yields well-calibrated p-values for controlling the false discovery rate and inferring multi-way interactions. We applied ELECT to both low and high resolution scHi-C datasets and carried out evaluations with external genomic and epigenomic data including data from DNA methylation, SPIRITE, scNanoHi-C, and DNA seqFISH+ assays. Application of ELECT to scHi-C data from human prefrontal cortex revealed multi-way interactions that involved GWAS SNPs associated with psychiatric disorders including autism and major depressive disorder, suggesting ELECTs potential for interrogating genomewide association studies for epistasis. ELECT is publicly available at https://github.com/keleslab/elect.