Implicit Hierarchical Tensor Decomposition of Single-Cell Four-Omics Data Reveals Cell-Type-Associated Enhancer--Promoter Regulatory Programs

Single-cell multi-omics approaches provide complementary insights into gene regulation, yet integrating diverse modalities such as enhancers, genes, and 3D genomic locations presents significant challenges. Researchers have now devised an implicit hierarchical tensor decomposition framework and utilized it to analyze the CHARM single-cell four-omics mouse brain dataset (GSE303006), which encompasses ATAC, H3K27ac, RNA, and reconstructed 3D enhancer-promoter (E-P) distance data.

Following quality control, the analysis retained 730,969 E-P pairs, 42,669 enhancers, 16,239 genes, 391,435 20-kb bin pairs, and 4,258 cells. Each modality was separately reduced to 20 components and mapped onto an implicit tensor with dimensions 730,969x4, 258x20x4, which was decomposed without constructing the full dataset. Out of the 100 largest Tucker core elements, all 12 cell components identified showed stronger cell-type effects than replicates (P=2.44 x 10-4, sign test).

One representative core connected the Inh_Ndnf/Lamp5-Ex_L3/4_IT cell axis to divergent presynaptic-transmission and developmental/morphogenetic E-P programs. Backprojection confirmed consistent ATAC, H3K27ac, and 3D effects across three biological replicates, while module-level RNA effects were less pronounced. This method uncovers the regulatory patterns that are common across multiple molecular modalities while remaining distinct from individual molecular data types.