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

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 between loci i and j from the contact probability 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 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 , 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.