MINTsC learns multi-way chromatin interactions from single cell high throughput chromatin conformation data.

A number of foundational analysis methods have emerged for scHi-C datasets capturing 3D organizations of genomes with pairwise measurements at the single cell or nuclei resolution; however, these datasets are currently under-utilized. The canonical analyses of scHi-C data encompass, beyond standard cell type identification, inference of chromosomal structures and pairwise interactions. However, multi-way chromatin interactions among genomic elements are often overlooked. Here, we introduce MINTsC, a framework to learn multi-way interactions from scHi-C. MINTsC builds on a dirichlet-multinomial spline model and yields multi-way interaction scores by aggregating pairwise interactions across cells of a context and summarizing them using order statistics of pairwise test statistics. MINTsC yields well-calibrated p-values for controlling the false discovery rate. Evaluation of MINTsC with scHi-C datasets from cell lines and complex tissues using multiple external genomic and epigenomic datasets support multi-way interactions inferred by MINTsC. Application of MINTsC to scHi-C data from human prefrontal cortex shows multi-way chromatin interactions, suggesting gene regulation by multiple enhancers. Most notably, MINTsC-inferred multi-way interactions demonstrate its potential for probing molecular QTL and association studies for epistatic SNP effects by substantially reducing the multiple-testing burden.