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

Abstract

Single-cell multi-omics provides complementary views of gene regulation, but integrating modalities with natural features comprising enhancers, genes, and three-dimensional (3D) genomic loci remains challenging. This study developed an implicit hierarchical tensor decomposition framework and applied it to the CHARM single-cell four-omics mouse brain data (GSE303006) by jointly analyzing ATAC, H3K27ac, RNA, and reconstructed 3D enhancer--promoter (E--P) distances. After quality control, 730,969 E--P pairs, 42,669 enhancers, 16,239 genes, 391,435 20-kb bin pairs, and 4,258 cells were retained. Each modality was independently reduced to 20 components and mapped to an implicit 730,969x4{,}258x20x4 tensor, which was decomposed without materializing the full array. In a joint model, cell type explained more variance than biological replicate for all 12 distinct cell components represented among the 100 largest Tucker core elements. A representative core linked the Inh_Ndnf/Lamp5--Ex_L3/4_IT cell axis to contrasting presynaptic-transmission and developmental/morphogenetic candidate E--P-associated programs. Its E--P and cell factors were recovered when the whole analysis was repeated independently on each pair of replicates, and the E--P pairs it prioritized agreed in direction with the cell-type-resolved enhancer--gene links of the original CHARM study. No single modality reproduced the program, which required the combination of accessibility, chromatin contact, and expression. Backprojection showed reproducible ATAC, H3K27ac, and 3D effects across three biological replicates; RNA differed clearly for the developmental module but not for the presynaptic module. The framework thus identifies regulatory structure that is shared across molecular modalities and is not recoverable from any single modality.