Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state—accessibility and amount of gene expression—of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.     

Higher-order chromatin structure: bridging physics and biology

Advances in microscopy and genomic techniques have provided new insight into spatial chromatin organization inside of the nucleus. In particular, chromosome conformation capture data has highlighted the relevance of polymer physics for high-order chromatin organization. In this context, we review basic polymer states, discuss how an appropriate polymer model can be determined from experimental data, and examine the success and limitations of various polymer models of higher-order interphase chromatin organization. By taking into account topological constraints acting on the chromatin fiber, recently developed polymer models of interphase chromatin can reproduce the observed scaling of distances between genomic loci, chromosomal territories, and probabilities of contacts between loci measured by chromosome conformation capture methods. Polymer models provide a framework for the interpretation of experimental data as ensembles of conformations rather than collections of loops, and will be crucial for untangling functional implications of chromosomal organization.     

Techniques for and challenges in reconstructing 3D genome structures from 2D chromosome conformation capture data

Chromosome conformation capture technologies that provide frequency information for contacts between genomic regions have been crucial for increasing our understanding of genome folding and regulation. However, such data do not provide direct evidence of the spatial 3D organization of chromatin. In this opinion article, we discuss the development and application of computational methods to reconstruct chromatin 3D structures from experimental 2D contact data, highlighting how such modeling provides biological insights and can suggest mechanisms anchored to experimental data. By applying different reconstruction methods to the same contact data, we illustrate some state-of-the-art of these techniques and discuss our gene resolution approach based on Brownian dynamics and Monte Carlo sampling.     

Light optical precision measurements of the active and inactive Prader-Willi syndrome imprinted regions in human cell nuclei

Despite the major advancements during the last decade with respect to both knowledge of higher order chromatin organization in the cell nucleus and the elucidation of epigenetic mechanisms of gene control, the true three-dimensional (3D) chromatin structure of endogenous active and inactive gene loci is not known. The present study was initiated as an attempt to close this gap. As a model case, we compared the chromatin architecture between the genetically active and inactive domains of the imprinted Prader-Willi syndrome (PWS) locus in human fibroblast and lymphoblastoid cell nuclei by 3D fluorescence in situ hybridization and quantitative confocal laser scanning microscopy. The volumes and 3D compactions of identified maternal and paternal PWS domains were determined in stacks of light optical serial sections using a novel threshold-independent approach. Our failure to detect volume and compaction differences indicates that possible differences are below the limits of light optical resolution. To overcome this limitation, spectral precision distance microscopy, a method of localization microscopy at the nanometer scale, was used to measure 3D distances between differentially labeled probes located both within the PWS region and in its neighborhood. This approach allows the detection of intranuclear differences between 3D distances down to about 70-90 nm, but again did not reveal clearly detectable differences between active and inactive PWS domains. Despite this failure, a comparison of the experimental 3D distance measurements with computer simulations of chromatin folding strongly supports a non-random higher order chromatin configuration of the PWS locus and argues against 3D configurations based on giant chromatin loops. Our results indicate that the search for differences between endogenous active and inactive PWS domains must be continued at still smaller scales than hitherto possible with conventional light microscopic procedures. The possibilities to achieve this goal are discussed.     

Uncovering the statistical physics of 3D chromosomal organization using data-driven modeling

In recent years, much effort has been devoted to understanding the three-dimensional (3D) organization of the genome and how genomic structure mediates nuclear function. The development of experimental techniques that combine DNA proximity ligation with high-throughput sequencing, such as Hi-C, have substantially improved our knowledge about chromatin organization. Numerous experimental advancements, not only utilizing DNA proximity ligation but also high-resolution genome imaging (DNA tracing), have required theoretical modeling to determine the structural ensembles consistent with such data. These 3D polymer models of the genome provide an understanding of the physical mechanisms governing genome architecture. Here, we present an overview of the recent advances in modeling the ensemble of 3D chromosomal structures by employing the maximum entropy approach combined with polymer physics. Particularly, we discuss the minimal chromatin model (MiChroM) along with the “maximum entropy genomic annotations from biomarkers associated with structural ensembles” (MEGABASE) model, which have been remarkably successful in the accurate modeling of chromosomes consistent with both Hi-C and DNA-tracing data.     

Three-dimensional genome organization in interphase and its relation to genome function

Higher order chromatin structure, i.e. the three-dimensional (3D) organization of the genome in the interphase nucleus, is an important component in the orchestration of gene expression in the mammalian genome. In this review we describe principles of higher order chromatin structure discussing three organizational parameters, i.e. chromatin folding, chromatin compaction and the nuclear position of the chromatin fibre. We argue that principles of 3D genome organization are probabilistic traits, reflected in a considerable cell-to-cell variation in 3D genome structure. It will be essential to understand how such higher order organizational aspects contribute to genome function to unveil global genome regulation.     

Distinct polymer physics principles govern chromatin dynamics in mouse and Drosophila topological domains

Background

In higher eukaryotes, the genome is partitioned into large "Topologically Associating Domains" (TADs) in which the chromatin displays favoured long-range contacts. While a crumpled/fractal globule organization has received experimental supports at higher-order levels, the organization principles that govern chromatin dynamics within these TADs remain unclear. Using simple polymer models, we previously showed that, in mouse liver cells, gene-rich domains tend to adopt a statistical helix shape when no significant locus-specific interaction takes place.

Results

Here, we use data from diverse 3C-derived methods to explore chromatin dynamics within mouse and Drosophila TADs. In mouse Embryonic Stem Cells (mESC), that possess large TADs (median size of 840 kb), we show that the statistical helix model, but not globule models, is relevant not only in gene-rich TADs, but also in gene-poor and gene-desert TADs. Interestingly, this statistical helix organization is considerably relaxed in mESC compared to liver cells, indicating that the impact of the constraints responsible for this organization is weaker in pluripotent cells. Finally, depletion of histone H1 in mESC alters local chromatin flexibility but not the statistical helix organization. In Drosophila, which possesses TADs of smaller sizes (median size of 70 kb), we show that, while chromatin compaction and flexibility are finely tuned according to the epigenetic landscape, chromatin dynamics within TADs is generally compatible with an unconstrained polymer configuration.

Conclusions

Models issued from polymer physics can accurately describe the organization principles governing chromatin dynamics in both mouse and Drosophila TADs. However, constraints applied on this dynamics within mammalian TADs have a peculiar impact resulting in a statistical helix organization.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1786-8) contains supplementary material, which is available to authorized users.     

Comparison of the three-dimensional organization of sperm and fibroblast genomes using the Hi-C approach

BackgroundThe three-dimensional organization of the genome is tightly connected to its biological function. The Hi-C approach was recently introduced as a method that can be used to identify higher-order chromatin interactions genome-wide. The aim of this study was to determine genome-wide chromatin interaction frequencies using the Hi-C approach in mouse sperm cells and embryonic fibroblasts.ResultsThe obtained data demonstrate that the three-dimensional genome organizations of sperm and fibroblast cells show a high degree of similarity both with each other and with the previously described mouse embryonic stem cells. Both A- and B-compartments and topologically associated domains are present in spermatozoa and fibroblasts. Nevertheless, sperm cells and fibroblasts exhibit statistically significant differences between each other in the contact probabilities of defined loci. Tight packaging of the sperm genome results in an enrichment of long-range contacts compared with the fibroblasts. However, only 30% of the differences in the number of contacts are based on differences in the densities of their genome packages; the main source of the differences is the gain or loss of contacts that are specific for defined genome regions. We find that the dependence of the contact probability on genomic distance for sperm is close to the dependence predicted for the fractal globular folding of chromatin.ConclusionsOverall, we can conclude that the three-dimensional structure of the genome is passed through generations without being dramatically changed in sperm cells.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-015-0642-0) contains supplementary material, which is available to authorized users.     

Probabilistic Prediction of Contacts in Protein-Ligand Complexes

We introduce a statistical method for evaluating atomic level 3D interaction patterns of protein-ligand contacts. Such patterns can be used for fast separation of likely ligand and ligand binding site combinations out of all those that are geometrically possible. The practical purpose of this probabilistic method is for molecular docking and scoring, as an essential part of a scoring function. Probabilities of interaction patterns are calculated conditional on structural x-ray data and predefined chemical classification of molecular fragment types. Spatial coordinates of atoms are modeled using a Bayesian statistical framework with parametric 3D probability densities. The parameters are given distributions a priori, which provides the possibility to update the densities of model parameters with new structural data and use the parameter estimates to create a contact hierarchy. The contact preferences can be defined for any spatial area around a specified type of fragment. We compared calculated contact point hierarchies with the number of contact atoms found near the contact point in a reference set of x-ray data, and found that these were in general in a close agreement. Additionally, using substrate binding site in cathechol-O-methyltransferase and 27 small potential binder molecules, it was demonstrated that these probabilities together with auxiliary parameters separate well ligands from decoys (true positive rate 0.75, false positive rate 0). A particularly useful feature of the proposed Bayesian framework is that it also characterizes predictive uncertainty in terms of probabilities, which have an intuitive interpretation from the applied perspective.     

Looping Probabilities in Model Interphase Chromosomes

Fluorescence in-situ hybridization (FISH) and chromosome conformation capture (3C) are two powerful techniques for investigating the three-dimensional organization of the genome in interphase nuclei. The use of these techniques provides complementary information on average spatial distances (FISH) and contact probabilities (3C) for specific genomic sites. To infer the structure of the chromatin fiber or to distinguish functional interactions from random colocalization, it is useful to compare experimental data to predictions from statistical fiber models. The current estimates of the fiber stiffness derived from FISH and 3C differ by a factor of 5. They are based on the wormlike chain model and a heuristic modification of the Shimada-Yamakawa theory of looping for unkinkable, unconstrained, zero-diameter filaments. Here, we provide an extended theoretical and computational framework to explain the currently available experimental data for various species on the basis of a unique, minimal model of decondensing chromosomes: a kinkable, topologically constraint, semiflexible polymer with the (FISH) Kuhn length of l_K = 300 nm, 10 kinks per Mbp, and a contact distance of 45 nm. In particular: 1), we reconsider looping of finite-diameter filaments on the basis of an analytical approximation (novel, to our knowledge) of the wormlike chain radial density and show that unphysically large contact radii would be required to explain the 3C data based on the FISH estimate of the fiber stiffness; 2), we demonstrate that the observed interaction frequencies at short genomic lengths can be explained by the presence of a low concentration of curvature defects (kinks); and 3), we show that the most recent experimental 3C data for human chromosomes are in quantitative agreement with interaction frequencies extracted from our simulations of topologically confined model chromosomes.     

G2 phase chromatin lacks determinants of replication timing

DNA replication in all eukaryotes follows a defined replication timing program, the molecular mechanism of which remains elusive. Using a Xenopus laevis egg extract replication system, we previously demonstrated that replication timing is established during early G1 phase of the cell cycle (timing decision point [TDP]), which is coincident with the repositioning and anchorage of chromatin in the newly formed nucleus. In this study, we use this same system to show that G2 phase chromatin lacks determinants of replication timing but maintains the overall spatial organization of chromatin domains, and we confirm this finding by genome-wide analysis of rereplication in vivo. In contrast, chromatin from quiescent cells retains replication timing but exhibits disrupted spatial organization. These data support a model in which events at the TDP, facilitated by chromatin spatial organization, establish determinants of replication timing that persist independent of spatial organization until the process of chromatin replication during S phase erases those determinants.     

101 Exploring the 3D spatial organization of the genome

Knowledge about the 3D organization of the genome will offer great insights into how cells retrieve and process the genetic information. Knowing the spatial probability distributions of individual genes will provide insights into gene regulatory and replication processes, and fill in the missing links between epigenomics, functional genomics, and structural biology. We will discuss an approach to determine 3D genome structures and structure–function maps of genomes by integrating divers types of data. To address the challenge of modeling highly variable genome structures, we discuss a population-based modeling approach, where we construct a large population of 3D genome structures that together are entirely consistent with all available experimental data including data from genome-wide chromosome conformation capture and imaging experiments. We interpret the result in terms of probabilities of a sample drawn from a population of heterogeneous structures. We will discuss results on the 3D spatial organization of genomes in human lymphoblastoid cells and budding yeast.     

Spatial preservation of nuclear chromatin architecture during three-dimensional fluorescence in situ hybridization (3D-FISH)

3D-FISH has become a major tool for studying the higher order chromatin organization in the cell nucleus. It is not clear, however, to what extent chromatin arrangement in the nucleus after fixation and 3D-FISH still reflects the order in living cells. To study this question, we compared higher order chromatin arrangements in living cells with those found after the 3D-FISH procedure. For in vivo studies we employed replication labeling of DNA with Cy3-conjugated nucleotides and/or chromatin labeling by GFP-tagged histone 2B. At the light microscope level, we compared the intranuclear distribution of H2B-GFP-tagged chromatin and the positions of replication-labeled chromatin domains in the same individual cells in vivo, after fixation with 4% paraformaldehyde, and after 3D-FISH. Light microscope data demonstrate a high degree of preservation of the spatial arrangement of approximately 1-Mb chromatin domains. Subsequent electron microscope investigations of chromatin structure showed strong alterations in the ultrastructure of the nucleus caused mainly by the heat denaturation step. Through this step chromatin acquires the appearance of a net with mesh size of 50-200 nm roughly corresponding to the average displacement of the chromatin domains observed at light microscope level. We conclude that 3D-FISH is a useful tool to study chromosome territory structure and arrangements down to the level of approximately 1-Mb chromatin domain positions. However, important ultrastructural details of the chromatin architecture are destroyed by the heat denaturation step, thus putting a limit to the usefulness of 3D-FISH analyses at nanometer scales.     

A method for simultaneously delineating multiple targets in 3D-FISH using limited channels, lasers, and fluorochromes

Many studies have suggested a link between the spatial organization of genomes and fundamental biological processes such as genome reprogramming, gene expression, and differentiation. Multicolor fluorescence in situ hybridization on three-dimensionally preserved nuclei (3D-FISH), in combination with confocal microscopy, has become an effective technique for analyzing 3D genome structure and spatial patterns of defined nucleus targets including entire chromosome territories and single gene loci. This technique usually requires the simultaneous visualization of numerous targets labeled with different colored fluorochromes. Thus, the number of channels and lasers must be sufficient for the commonly used labeling scheme of 3D-FISH, “one probe-one target”. However, these channels and lasers are usually restricted by a given microscope system. This paper presents a method for simultaneously delineating multiple targets in 3D-FISH using limited channels, lasers, and fluorochromes. In contrast to other labeling schemes, this method is convenient and simple for multicolor 3D-FISH studies, which may result in widespread adoption of the technique. Lastly, as an application of the method, the nucleus locations of chromosome territory 18/21 and centromere 18/21/13 in normal human lymphocytes were analyzed, which might present evidence of a radial higher order chromatin arrangement.     

NucleoMap: A computational tool for identifying nucleosomes in ultra-high resolution contact maps

Although poorly positioned nucleosomes are ubiquitous in the eukaryotic genome, they are difficult to identify with existing nucleosome identification methods. Recently available enhanced high-throughput chromatin conformation capture techniques such as Micro-C, DNase Hi-C, and Hi-CO characterize nucleosome-level chromatin proximity, probing the positions of mono-nucleosomes and the spacing between nucleosome pairs at the same time, enabling nucleosome profiling in poorly positioned regions. Here we develop a novel computational approach, NucleoMap, to identify nucleosome positioning from ultra-high resolution chromatin contact maps. By integrating nucleosome read density, contact distances, and binding preferences, NucleoMap precisely locates nucleosomes in both prokaryotic and eukaryotic genomes and outperforms existing nucleosome identification methods in both precision and recall. We rigorously characterize genome-wide association in eukaryotes between the spatial organization of mono-nucleosomes and their corresponding histone modifications, protein binding activities, and higher-order chromatin functions. We also find evidence of two tetra-nucleosome folding structures in human embryonic stem cells and analyze their association with multiple structural and functional regions. Based on the identified nucleosomes, nucleosome contact maps are constructed, reflecting the inter-nucleosome distances and preserving the contact distance profiles in original contact maps.