From Hi-C Contact Map to Three-dimensional Organization of Interphase Human Chromosomes

Abstract

The probabilities that two loci in chromosomes that are separated by a certain genome length can be inferred using chromosome conformation capture method and related Hi-C experiments. How to go from such maps to an ensemble of three-dimensional structures, which is an important step in understanding the way nature has solved the packaging of the hundreds of million base pair chromosomes in tight spaces, is an open problem. We created a theory based on polymer physics and the maximum entropy principle, leading to the HIPPS (Hi-C-Polymer-Physics-Structures) method allows us to go from contact maps to 3D structures. It is difficult to calculate the mean distance ( rij ) between loci i and j from the contact probability ( pij ) because the contact exists only in a fraction (unknown) of cell populations. Despite this massive heterogeneity, we first prove that there is a theoretical lower bound connecting pij and rij via a power-law relation. We show, using simulations of a precisely solvable model, that the overall organization is accurately captured by constructing the distance map from the contact map even when the cell population is heterogeneous, thus justifying the use of the lower bound. Building on these results and using the mean distance matrix, whose elements are rij , we use maximum entropy principle to reconstruct the joint distribution of spatial positions of the loci, which creates an ensemble of structures for the 23 chromosomes from lymphoblastoid cells. The HIPPS method shows that the conformations of a given chromosome are highly heterogeneous even in a single cell type. Nevertheless, the differences in the heterogeneity of the same chromosome in different cell types (normal as well as cancerous cells) can be quantitatively discerned using our theory.

Generation of dynamic three-dimensional genome structure through phase separation of chromatin

“…In particular, the H3K9 methylated nucleosomes in heterochromatin-like type-B regions bind HP1 proteins, which glue nucleosomes to induce the effective attraction between nucleosomes ( 35 , 36 ). Hence, the previous computational models assumed attractive interactions between coarse-grained (CG) heterochromatin-like regions ( 12 – 15 , 22 , 27 ). However, the effective interactions between CG regions consisting of hundreds of nucleosomes may differ from those between individual nucleosomes.…”

“…For further clarifying the mechanisms of genome organization, it is necessary to develop reliable computational models that can bridge these different experimental paradigms. Computational polymer models of individual chromosomes and their complexes were developed using the Hi-C data of global chromatin contacts as the input to deduce the knowledge-based forces on chromatin ( 12 – 15 ). More refined input data such as the global genome-wide contact pattern in the single-cell Hi-C data were necessary for modeling the whole-genome structure of mouse and human cells ( 16 – 18 ).…”

Phase Separation and Correlated Motions in Motorized Genome

“…Interaction parameters in the ideal and compartment potential were tuned to reproduce various average contact probabilities determined from Hi-C experiments for GM12878 cells using the maximum entropy optimization algorithm. 58,60–62…”

“…Interaction parameters in the ideal and compartment potential were tuned to reproduce various average contact probabilities determined from Hi-C experiments for GM12878 cells using the maximum entropy optimization algorithm. 58,[60][61][62] We carried out Brownian dynamics simulations of the coarse-grained model to produce an ensemble of genome structures (see Methods Section for simulation details). These structures support the formation of territories, and individual chromosomes exhibit collapsed conformations with minimal intermingling among them (Figure S1).…”

Structural changes in chromosomes driven by multiple condensin motors during mitosis

“…To assess if the bump in P ( s ) could be reproduced, and explained in terms of helical (or related) conformations, we used the recently developed HIPPS method (Shi and Thirumalai 2021). As a complement to the A-GRMC simulations and to compare the extent of helix formation in DT40 and HeLa cells, we calculated the P ( s ) at different time points as the cell transitions from the interphase to the mitotic phase using the HIPPS method, which predicts an ensemble of 3D chromosome structures with the measured Hi-C maps as the only input (see Methods).…”