Heterogeneous Loop Model to Infer 3D Chromosome Structures from Hi-C

Hi-C-guided many-polymer model to decipher 3D genome organization

We propose a high-throughput chromosome conformation capture data-based many-polymer model that allows us to generate an ensemble of multi-scale genome structures. We demonstrate the efficacy of our model by validating the generated structures against experimental measurements and employ them to address key questions regarding genome organization. Our model first confirms a significant correlation between chromosome size and nuclear positioning. Specifically, smaller chromosomes are distributed at the core region, whereas larger chromosomes are at the periphery, interacting with the nuclear envelope. The spatial distribution of A- and B-type compartments, which is nontrivial to infer from the corresponding high-throughput chromosome conformation capture maps alone, can also be elucidated using our model, accounting for an issue such as the effect of chromatin-lamina interaction on the compartmentalization of conventional and inverted nuclei. In accordance with imaging data, the overall shape of the 3D genome structures generated from our model displays significant variation. As a case study, we apply our method to the yellow fever mosquito genome, finding that the predicted morphology displays, on average, a more globular shape than the previously suggested spindle-like organization and that our prediction better aligns with the fluorescence in situ hybridization data. Our model has great potential to be extended to investigate many outstanding issues concerning 3D genome organization.

Chromatin image-driven modelling

The challenge of modelling the spatial conformation of chromatin remains an open problem. While multiple data-driven approaches have been proposed, each has limitations. This work introduces two image-driven modelling methods based on the Molecular Dynamics Flexible Fitting (MDFF) approach: the force method and the correlational method. Both methods have already been used successfully in protein modelling. We propose a novel way to employ them for building chromatin models directly from 3D images. This approach is termed image-driven modelling. Additionally, we introduce the initial structure generator, a tool designed to generate optimal starting structures for the proposed algorithms. The methods are versatile and can be applied to various data types, with minor modifications to accommodate new generation imaging techniques.

Footprints of loop extrusion in statistics of intra-chromosomal distances: An analytically solvable model

Active loop extrusion-the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes-is a firmly established mechanism responsible for chromatin spatial organization at different stages of a cell cycle in eukaryotes and bacteria. The theoretical insight into the effect of loop extrusion on the experimentally measured statistics of chromatin conformation can be gained with an appropriately chosen polymer model. Here, we consider the simplest analytically solvable model of an interphase chromosome, which is treated as an ideal chain with disorder of sufficiently sparse random loops whose conformations are sampled from the equilibrium ensemble. This framework allows us to arrive at the closed-form analytical expression for the mean-squared distance between pairs of genomic loci, which is valid beyond the one-loop approximation in diagrammatic representation. In addition, we analyze the loop-induced deviation of chain conformations from the Gaussian statistics by calculating kurtosis of probability density of the pairwise separation vector. The presented results suggest the possible ways of estimating the characteristics of the loop extrusion process based on the experimental data on the scale-dependent statistics of intra-chromosomal pair-wise distances.

LoopSage: An energy-based Monte Carlo approach for the loop extrusion modeling of chromatin

The connection between the patterns observed in 3C-type experiments and the modeling of polymers remains unresolved. This paper presents a simulation pipeline that generates thermodynamic ensembles of 3D structures for topologically associated domain (TAD) regions by loop extrusion model (LEM). The simulations consist of two main components: a stochastic simulation phase, employing a Monte Carlo approach to simulate the binding positions of cohesins, and a dynamical simulation phase, utilizing these cohesins' positions to create 3D structures. In this approach, the system's total energy is the combined result of the Monte Carlo energy and the molecular simulation energy, which are iteratively updated. The structural maintenance of chromosomes (SMC) protein complexes are represented as loop extruders, while the CCCTC-binding factor (CTCF) locations on DNA sequence are modeled as energy minima on the Monte Carlo energy landscape. Finally, the spatial distances between DNA segments from ChIA-PET experiments are compared with the computer simulations, and we observe significant Pearson correlations between predictions and the real data. LoopSage model offers a fresh perspective on chromatin loop dynamics, allowing us to observe phase transition between sparse and condensed states in chromatin.

On the Advent of Super-Resolution Microscopy in the Realm of Polycomb Proteins

The genomes of metazoans are organized at multiple spatial scales, ranging from the double helix of DNA to whole chromosomes. The intermediate genomic scale of kilobases to megabases, which corresponds to the 50-300 nm spatial scale, is particularly interesting, as the 3D arrangement of chromatin is implicated in multiple regulatory mechanisms. In this context, polycomb group (PcG) proteins stand as major epigenetic modulators of chromatin function, acting prevalently as repressors of gene transcription by combining chemical modifications of target histones with physical crosslinking of distal genomic regions and phase separation. The recent development of super-resolution microscopy (SRM) has strongly contributed to improving our comprehension of several aspects of nano-/mesoscale (10-200 nm) chromatin domains. Here, we review the current state-of-the-art SRM applied to PcG proteins, showing that the application of SRM to PcG activity and organization is still quite limited and mainly focused on the 3D assembly of PcG-controlled genomic loci. In this context, SRM approaches have mostly been applied to multilabel fluorescence in situ hybridization (FISH). However, SRM data have complemented the maps obtained from chromosome capture experiments and have opened a new window to observe how 3D chromatin topology is modulated by PcGs.

Dissecting the cosegregation probability from genome architecture mapping

Genome architecture mapping (GAM) is a recently developed methodology that offers the cosegregation probability of two genomic segments from an ensemble of thinly sliced nuclear profiles, enabling us to probe and decipher three-dimensional chromatin organization. The cosegregation probability from GAM binned at 1 Mb, which thus probes the length scale associated with the genomic separation greater than 1 Mb, is, however, not identical to the contact probability obtained from Hi-C, and its correlation with interlocus distance measured with fluorescence in situ hybridization is not so good as the contact probability. In this study, by using a polymer-based model of chromatins, we derive a theoretical expression of the cosegregation probability as well as that of the contact probability and carry out quantitative analyses of how they differ from each other. The results from our study, validated with in silico GAM analysis on three-dimensional genome structures from fluorescence in situ hybridization, suggest that to attain strong correlation with the interlocus distance, a properly normalized version of cosegregation probability needs to be calculated based on a large number of nuclear slices (n>103).

Extracting multi-way chromatin contacts from Hi-C data

There is a growing realization that multi-way chromatin contacts formed in chromosome structures are fundamental units of gene regulation. However, due to the paucity and complexity of such contacts, it is challenging to detect and identify them using experiments. Based on an assumption that chromosome structures can be mapped onto a network of Gaussian polymer, here we derive analytic expressions for n-body contact probabilities (n > 2) among chromatin loci based on pairwise genomic contact frequencies available in Hi-C, and show that multi-way contact probability maps can in principle be extracted from Hi-C. The three-body (triplet) contact probabilities, calculated from our theory, are in good correlation with those from measurements including Tri-C, MC-4C and SPRITE. Maps of multi-way chromatin contacts calculated from our analytic expressions can not only complement experimental measurements, but also can offer better understanding of the related issues, such as cell-line dependent assemblies of multiple genes and enhancers to chromatin hubs, competition between long-range and short-range multi-way contacts, and condensates of multiple CTCF anchors.

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

Chromosomes are giant chain molecules organized into an ensemble of three-dimensional structures characterized with its genomic state and the corresponding biological functions. Despite the strong cell-to-cell heterogeneity, the cell-type specific pattern demonstrated in high-throughput chromosome conformation capture (Hi-C) data hints at a valuable link between structure and function, which makes inference of chromatin domains (CDs) from the pattern of Hi-C a central problem in genome research. Here we present a unified method for analyzing Hi-C data to determine spatial organization of CDs over multiple genomic scales. By applying statistical physics-based clustering analysis to a polymer physics model of the chromosome, our method identifies the CDs that best represent the global pattern of correlation manifested in Hi-C. The multi-scale intra-chromosomal structures compared across different cell types uncover the principles underlying the multi-scale organization of chromatin chain: (i) Sub-TADs, TADs, and meta-TADs constitute a robust hierarchical structure. (ii) The assemblies of compartments and TAD-based domains are governed by different organizational principles. (iii) Sub-TADs are the common building blocks of chromosome architecture. Our physically principled interpretation and analysis of Hi-C not only offer an accurate and quantitative view of multi-scale chromatin organization but also help decipher its connections with genome function.

An array of square blocks and checkerboard patterns characteristic to Hi-C data reflects the multi-scale organization of the chromatin chain. Deciphering the structures of chromatin domains from Hi-C and associating them with genome function are open problems of great importance in genome research. However, most existing methods are specialized in finding domains at different scales, making it difficult to integrate the solutions. Here we develop a unified framework for modeling and inferring domain structures over multiple scales, based on a physical model of the chromosome that reflects its nature as a three-dimensional object. Our method efficiently explores the space of domain solutions at different genomic scales, and systematically infers the chromatin domains over multiple scales from Hi-C data by employing a single tuning parameter. Our principled interpretation of Hi-C not only offers a quantitative view of multi-scale chromatin organization but also helps understand its connections with genome function.

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

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.

Toward understanding the dynamic state of 3D genome

The three-dimensional (3D) genome organization and its role in biological activities have been investigated for over a decade in the field of cell biology. Recent studies using live-imaging and polymer simulation have suggested that the higher-order chromatin structures are dynamic; the stochastic fluctuations of nucleosomes and genomic loci cannot be captured by bulk-based chromosome conformation capture techniques (Hi-C). In this review, we focus on the physical nature of the 3D genome architecture. We first describe how to decode bulk Hi-C data with polymer modeling. We then introduce our recently developed PHi-C method, a computational tool for modeling the fluctuations of the 3D genome organization in the presence of stochastic thermal noise. We also present another new method that analyzes the dynamic rheology property (represented as microrheology spectra) as a measure of the flexibility and rigidity of genomic regions over time. By applying these methods to real Hi-C data, we highlighted a temporal hierarchy embedded in the 3D genome organization; chromatin interaction boundaries are more rigid than the boundary interior, while functional domains emerge as dynamic fluctuations within a particular time interval. Our methods may bridge the gap between live-cell imaging and Hi-C data and elucidate the nature of the dynamic 3D genome organization.

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

The one-dimensional information of genomic DNA is hierarchically packed inside the eukaryotic cell nucleus and organized in a three-dimensional (3D) space. Genome-wide chromosome conformation capture (Hi-C) methods have uncovered the 3D genome organization and revealed multiscale chromatin domains of compartments and topologically associating domains (TADs). Moreover, single-nucleosome live-cell imaging experiments have revealed the dynamic organization of chromatin domains caused by stochastic thermal fluctuations. However, the mechanism underlying the dynamic regulation of such hierarchical and structural chromatin units within the microscale thermal medium remains unclear. Microrheology is a way to measure dynamic viscoelastic properties coupling between thermal microenvironment and mechanical response. Here, we propose a new, to our knowledge, microrheology for Hi-C data to analyze the dynamic compliance property as a measure of rigidness and flexibility of genomic regions along with the time evolution. Our method allows the conversion of an Hi-C matrix into the spectrum of the dynamic rheological property along the genomic coordinate of a single chromosome. To demonstrate the power of the technique, we analyzed Hi-C data during the neural differentiation of mouse embryonic stem cells. We found that TAD boundaries behave as more rigid nodes than the intra-TAD regions. The spectrum clearly shows the dynamic viscoelasticity of chromatin domain formation at different timescales. Furthermore, we characterized the appearance of synchronous and liquid-like intercompartment interactions in differentiated cells. Together, our microrheology data derived from Hi-C data provide physical insights into the dynamics of the 3D genome organization.

Maximum parsimony interpretation of chromatin capture experiments

We present a new approach to characterizing the global geometric state of chromatin from HiC data. Chromatin conformation capture techniques (3C, and its variants: 4C, 5C, HiC, etc.) probe the spatial structure of the genome by identifying physical contacts between genomic loci within the nuclear space. In whole-genome conformation capture (HiC) experiments, the signal can be interpreted as spatial proximity between genomic loci and physical distances can be estimated from the data. However, observed spatial proximity signal does not directly translate into persistent contacts within the nuclear space. Attempts to infer a single conformation of the genome within the nuclear space lead to internal geometric inconsistencies, notoriously violating the triangle inequality. These inconsistencies have been attributed to the stochastic nature of chromatin conformation or to experimental artifacts. Here we demonstrate that it can be explained by a mixture of cells, each in one of only several conformational states, contained in the sample. We have developed and implemented a graph-theoretic approach that identifies the properties of such postulated subpopulations. We show that the geometrical conflicts in a standard yeast HiC dataset, can be explained by only a small number of homogeneous populations of cells (4 populations are sufficient to reconcile 95,000 most prominent impossible triangles, 8 populations can explain 375,000 top geometric conflicts). Finally, we analyze the functional annotations of genes differentially interacting between the populations, suggesting that each inferred subpopulation may be involved in a functionally different transcriptional program.