A maximum-entropy model to predict 3D structural ensembles of chromatins from pairwise distances: Applications to Interphase Chromosomes and Structural Variants

ABSTRACT The principles that govern the organization of genomes, which are needed for a deeper understanding of how chromosomes are packaged and function in eukaryotic cells, could be deciphered if the three dimensional (3D) structures are known. Recently, single-cell imaging experiments have determined the 3D coordinates of a number of loci in a chromosome. Here, we introduce a computational method (Distance Matrix to Ensemble of Structures, DIMES), based on the maximum entropy principle, with experimental pair-wise distances between loci as constraints, to generate a unique ensemble of 3D chromatin structures. Using the ensemble of structures, we quantitatively account for the distribution of pair-wise distances, three-body co-localization and higher-order interactions. We demonstrate that the DIMES method can be applied to both small length-scale and chromosome-scale imaging data to quantify the extent of heterogeneity and fluctuations in the shapes on various length scales. We develop a perturbation method that is used in conjunction with DIMES to predict the changes in 3D structures from structural variations. Our method also reveals quantitative differences between the 3D structures inferred from Hi-C and the ones measured in imaging experiments. Finally, the physical interpretation of the parameters extracted from DIMES provides insights into the origin of phase separation between euchromatin and heterochromatin domains.