A maximum-entropy model to predict 3D structural ensembles of chromatin from pairwise distances with applications to interphase chromosomes and structural variants

Abstract

The principles that govern the organization of genomes, which are needed for an 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 techniques have been developed to determine the 3D coordinates of genomic loci in vivo. Here, we introduce a computational method (Distance Matrix to Ensemble of Structures, DIMES), based on the maximum entropy principle, with experimental pairwise 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 pairwise distances, three-body co-localization, and higher-order interactions. The DIMES method can be applied to both small and chromosome-scale imaging data to quantify the extent of heterogeneity and fluctuations in the shapes across various length scales. We develop a perturbation method 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 those 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.

Identification of Two Subsets of Subcompartment A1 Associated with High Transcriptional Activity and Frequent Loop Extrusion

“…Data in hic format were converted to the cooler format by using the hic2cool ( , accessed on 12 January 2023) at the resolution of 25,000 base pairs. The HIPPS-DIMEs software package [ 52 ] was then used to simulate three-dimensional chromosome organization. For Figure 1 A, the iteration number was set to 10, while for others, it was set to 1000.…”

Dynamics of chromosome organization in a minimal bacterial cell

“…Following the creation of 3C, many variations have been developed (Denker and de Laat, 2016;Goel and Hansen, 2020), the most well-known of which is perhaps Hi-C (Lieberman-Aiden et al, 2009). Although researchers have a stunning breadth of experimental data characterizing interactions throughout the genome, computational models (Rosa and Zimmer, 2014;Tiana and Giorgetti, 2019) are required to solve the inverse problem of determining 3D genome organization (Di Pierro et al, 2017;Messelink et al, 2021;Shi and Thirumalai, 2023) and provide mechanistic insights (Sanborn et al, 2015;Fudenberg et al, 2016;Banigan et al, 2020;Fiorillo et al, 2021). i ), twisting (U t i ), aligning (U a i ), and stretching (U s i ) potential energy functions for intramonomer interactions, and potential energy functions for excluded-volume interactions (U e.v.…”