MaxComp: Predicting single-cell chromatin compartments from 3D chromosome structures

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.Author summary: Chromosome conformation capture and imaging techniques have revealed that the genome spatially segregates into at least two functional compartments. Ensemble Hi-C contact frequency maps display checkerboard-like patterns, indicating that chromatin regions fall into two major compartments—likely a result of phase separation—where regions within the same compartment preferentially interact, often over long genomic distances, while interactions with the opposite compartment are minimized. Principal component analysis (PCA) of ensemble Hi-C data is commonly used to identify these compartments. However, because the compartment annotations are derived from a cell population, this method cannot provide information about compartments in single cells. In this study, we introduce an unsupervised graph-based method to predict A/B compartments in single cells, which utilizes only structural information in single cells. Our results demonstrate that ensemble PCA-based compartment annotations can be reproduced as population averages of our single-cell predictions. Our results reveal substantial cell-to-cell heterogeneity in compartmentalization, with notable variability across genomic regions. Applying our method to multiplexed FISH tracing data links single-cell compartment annotations with gene transcriptional activity, and enables exploration of how local chromatin structure relates to compartment identity. Compared to existing methods, our approach achieves superior compartmentalization scores, offering a robust and interpretable framework for analyzing genome architecture in single cells.