Abstract
The probability of two loci, separated by a certain genome length, being in contact can be inferred using the Chromosome Conformation Capture (3C) method and related Hi-C experiments. How to go from the contact map, a matrix listing the mean contact probabilities between a large number of pairs of loci, to an ensemble of three-dimensional structures is an open problem. A solution to this problem, without assuming an assumed energy function, would be the first step in understanding the way nature has solved the packaging of chromosomes in tight cellular spaces. We created a theory, based on polymer physics characteristics of chromosomes and the maximum entropy principles, referred to as HIPPS (Hi-C-Polymer-Physics-Structures) method, that allows us to calculate the 3D structures solely from Hi-C contact maps. We created an ensemble of 3D structures for the 23 chromosomes from lymphoblastoid cells using the measured contact maps as inputs. The HIPPS method shows that conformations of chromosomes are heterogeneous even in a single cell type. The differences in the conformational heterogeneity of the same chromosome in different cell types (normal as well as cancerous cells) can also be quantitatively discerned using our theory. We validate the method by showing that the calculated volumes of the 23 chromosomes from the predicted 3D structures are in good agreement with experimental estimates. Because the method is general, the 3D structures for any species may be calculated directly from the contact map without the need to assume a specific polymer model, as is customarily done.
Highlights
The question of how chromosomes are packed in the tight space of the cell nucleus has taken center stage in genome biology, largely due to the spectacular advances in experimental techniques
Even if one were to construct polymer models that produce results that are consistent with Hi-C contact maps, certain features of the chromosome structures would be discordant with the fluorescence in situ hybridization (FISH) data, reflecting the heterogeneous genome organization [26]
The value ηm;ij, KðrijÞ, or QðpijÞ in Eqs. (2)–(5) in principle could be extracted from the distribution of hriji, which can be measured using imaging techniques. This is usually unavailable or the data are sparse, which leads to the question: Despite the lack of knowledge of the composition of the cell populations, can we provide an approximate but reasonably accurate relation between hpiji and hriji? In other words, rather than answer the question (a) posed in the previous section precisely, as we did for the homogeneous generalized Rouse model for chromosomes (GRMC), we are seeking an approximate solution
Summary
The question of how chromosomes are packed in the tight space of the cell nucleus has taken center stage in genome biology, largely due to the spectacular advances in experimental techniques. We do not assume any energy function, but use characteristics that describe the polymeric properties of the chromosomes to generate the distance map, which is used in conjunction with the maximum entropy principle to construct 3D structures from Hi-C data. Elsewhere [8], we showed that because a given contact is present only in certain cells (PH), a one-to-one relation between contact probability and spatial distance between a pair of loci does not exist. Even if one were to construct polymer models that produce results that are consistent with Hi-C contact maps, certain features of the chromosome structures would be discordant with the FISH data, reflecting the heterogeneous genome organization [26]. The HIPPS method can detect the differences in the extent of CH of a specific chromosome between normal and cancer cells
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