Prediction of single-cell chromatin compartments from single-cell chromosome structures by MaxComp
Authors: Zhan Yuxiang , Musella Francesco , Alber Frank 
Published: July 2024

The genome is partitioned into distinct chromatin compartments with at least two main classes, a transcriptionally activeAand an inactiveBcompartment, 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/Bcompartments 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-cellA/Bcompartments 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.

Author Summary

Chromosome conformation capture and imaging techniques revealed the segregation of genomic chromatin into at least two functional compartments. Hi-C contact frequency matrices show checkerboard-like patterns indicating that chromatin regions are divided into at least two states, possibly a result of phase separation. Chromatin regions in the same state have preferential interactions with each other, often over extended sequence distances, while interactions to regions in the opposing state are minimized. Principal component analysis (PCA) on ensemble Hi-C contact frequency matrices can identify these compartment states. However, because the compartment annotations are derived from a cell population, this method cannot provide information about compartments in single cells. Here in this study, we introduce an unsupervised method to predict single-cell compartments using graph-based programming, which utilizes only structural information in single cells. Our results demonstrate that PCA-based ensemble compartment annotations can be reproduced as population averages of our single-cell compartment predictions. Moreover, our results reveal the cell-to-cell heterogeneity of compartments in a cell population, which shows significant disparities among different chromatin regions. Moreover, by applying our approach to multiplexed FISH tracing experiments, our method reveals the relationship between single-cell compartment annotations and gene transcriptional activity in single cells. Finally, our approach also allows us to relate chromatin structural features in single cells with compartment properties. Comparison with other existing approaches showed that our method produces overall better compartmentalization scores in single cells.