Prediction of single-cell chromatin compartments from single-cell chromosome structures by MaxComp

The genome is partitioned into distinct chromatin compartments with at least two main classes, a transcriptionally active A and an inactive B compartment, corresponding mostly to the segregation of euchromatin and heterochromatin. Chromatin within the same compartment has a higher tendency to interact with itself than with regions in opposing compartments. A/B compartments are traditionally derived from ensemble Hi-C contact matrices through principal component analysis of their covariance matrices. However, defining compartments in single cells from single-cell Hi-C maps is non trivial due to sparsity of the data and the fact that homologous copies are typically not resolved. Here we present an unsupervised approach, named MaxComp, to determine single-cell A/B compartments from geometric considerations in 3D chromosome structures, either from multiplexed FISH imaging or from models derived from Hi-C data. By representing each single-cell structure as an undirected graph with edge-weights encoding structural information, the problem of predicting chromosome compartments can be transformed to an alternative form of the Max-cut problem, a semidefinite graph programming method (SPD) to determine an optimal division of a chromosome structure graph into two structural compartments. Our results show that compartment annotations from principal component analysis of ensemble Hi-C data can be perfectly reproduced as population averages of our single-cell compartment predictions. We therefore prove that compartment predictions can be achieved from geometric considerations alone using 3D coordinates of chromatin regions together with information about their nuclear microenvironment. Our results reveal substantial cell-to-cell heterogeneity of compartments in a cell population, which substantially differs between individual genomic regions. Moreover, by applying our approach to multiplexed FISH tracing experiments, our method sheds light on the relationship between single-cell compartment annotations and gene transcriptional activity in single cells. Overall our approach provides new insights into single-cell chromatin condensation, relationship between population and single-cell chromatin compartmentalization, the cell-to-cell variations of chromatin compartments and its impact on gene transcription.