Revisiting the organization of Polycomb-repressed domains: 3D chromatin models from Hi-C compared with super-resolution imaging

Abstract

The accessibility of target gene, a factor critical for gene regulation, is controlled by epigenetic fine-tuning of chromatin organization. While there are multiple experimental techniques to study change of chromatin architecture with its epigenetic state, measurements from them are not always complementary. A qualitative discrepancy is noted between recent super-resolution imaging studies, particularly on Polycomb-group protein repressed domains in Drosophila cell. One of the studies shows that Polycomb-repressed domains are more compact than inactive domains and are segregated from neighboring active domains, whereas Hi-C and chromatin accessibility assay as well as the other super-resolution imaging studies paint a different picture. To examine this issue in detail, we analyzed Hi-C libraries of Drosophila chromosomes as well as distance constraints from one of the imaging studies, and modeled different epigenetic domains by employing a polymer-based approach. According to our chromosome models, both Polycomb-repressed and inactive domains are featured with a similar degree of intra-domain packaging and significant intermixing with adjacent active domains. The epigenetic domains explicitly visualized by our polymer model call for extra attention to the discrepancy of the super-resolution imaging with other measurements, although its precise physicochemical origin still remains to be elucidated.

Extracting multi-way chromatin contacts from Hi-C data

“…Numerical details for determining the stiffness matrix K * Our previous numerical procedure [50,51] to determine K * -matrix has been improved in this paper by adapting those in the recent modeling studies of chromatin by two other groups [71][72][73]. The best solution, K * , which is consistent with a given Hi-C data, was determined with Hi-C data by optimizing the cost function, K * = arg min K L(K) (see Fig 2).…”

A unified framework for inferring the multi-scale organization of chromatin domains from Hi-C

“…Use of the Gaussian polymer network model was motivated by an observation, from fluorescence measurements, that the spatial distances between pairs of chromatin segments are well described by the gaussian distribution [21,[42][43][44] (see S1 Fig). This observation suggests that, despite the presence of cell-to-cell variation in a population of cells [39,[45][46][47][48][49][50][51], we can still approximate the chromosome with a gaussian polymer network whose configuration fluctuates around a local basin of mechanical equilibrium [16,41,[52][53][54][55], for the purpose of modeling the pairwise distances. See S1 Appendix for more discussion.…”

“…that chromosomes are a hierarchically structured three dimensional object made of a long polymer [8,16,[35][36][37][38][39][40][41].…”

“…Progress was made by methods that consider hierarchical CDs [ 33 , 34 ]; however, these method fall short of providing a common interpretable framework, because they are restricted to local pattern recognitions, as in many earlier methods [ 18 , 19 , 22 , 32 ]. To avoid the arbitrariness of focusing on the features at specific scales, a better approach will be to start from a physically principled notion that chromosomes are a hierarchically structured three dimensional object made of a long polymer [ 8 , 16 , 35 – 41 ].…”

Extracting multi-way chromatin contacts from Hi-C data

“…Since the polymer physics idea was first used to explore the physical characteristics of chromosomes as long polymer chains confined in a small nuclear space [28,[31][32][33][34][35][36][37][38], computational strategies of incorporating genomic constraints from experimental measurements and epigenomic information into polymer-based modeling of 3D chromosome structure have recently gained much traction [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Many studies, which generate an ensemble of 3D chromosome structures, highlight the heterogeneous and probabilistic nature of chromosome structure [45,47,50,51,54]. Once an ensemble of structural models of chromosomes are obtained from computational approaches, it is straightforward to count the multi-way chromatin contacts directly from them and to quantify the corresponding contact probabilities.…”