Abstract
The genome is organized into distinct chromatin compartments with at least two main classes, a transcriptionally active A and an inactive B compartment, broadly corresponding to euchromatin and heterochromatin. Chromatin regions within the same compartment preferentially interact with each other over regions in the opposite compartment. A/B compartments are traditionally identified from ensemble Hi-C contact frequency matrices using principal component analysis of their covariance matrices. However, defining compartments at the single-cell level from sparse single-cell Hi-C data is challenging, especially since homologous copies are often not resolved. To address this, we present MaxComp, an unsupervised method, for inferring single-cell A/B compartments based on 3D geometric considerations in single-cell chromosome structures-derived either from multiplexed FISH-omics imaging or 3D structure models derived from Hi-C data. By representing each 3D chromosome structure as an undirected graph with edge-weights encoding structural information, MaxComp reformulates compartment prediction as a variant of the Max-cut problem, solved using semidefinite graph programming (SPD) to optimally partition the graph into two structural compartments. Our results show that the population average of MaxComp single-cell compartment annotations closely matches those derived from ensemble Hi-C principal component analysis, demonstrating that compartmentalization can be recovered from geometric principles alone, using only the 3D coordinates and nuclear microenvironment of chromatin regions. Our approach reveals widespread cell-to-cell variability in compartment organization, with substantial heterogeneity across genomic loci. When applied to multiplexed FISH imaging data, MaxComp also uncovers relationships between compartment annotations and transcriptional activity at the single-cell level. In summary, MaxComp offers a new framework for understanding chromatin compartmentalization in single cells, connecting 3D genome architecture, and transcriptional activity with the cell-to-cell variations of chromatin compartments.