Perspectives: using polymer modeling to understand the formation and function of nuclear compartments

Multivalent nucleosome scaffolding by bromodomain and extraterminal domain tandem bromodomains

Promoter-promoter and enhancer-promoter interactions are enriched in histone acetylation and central to chromatin organization in active genetic regions. Bromodomains are epigenetic 'readers' that recognize and bind histone acetylation. Bromodomains often exist in tandem or with other reader domains. Cellular knockdown of the bromodomain and extraterminal domain (BET) protein family disrupts chromatin organization, but the mechanisms through which BET proteins preserve chromatin structure are largely unknown. We hypothesize that BET proteins maintain overall chromatin structure by employing their tandem bromodomains to multivalently scaffold acetylated nucleosomes in an intra- or internucleosomal manner. To test this hypothesis biophysically, we used small-angle X-ray scattering, electron paramagnetic resonance, and Rosetta protein modeling to show that a disordered linker separates BET tandem bromodomain acetylation binding sites by 15-157 Å. Most of these modeled distances are sufficient to span the length of a nucleosome (>57 Å). Focusing on the BET family member BRD4, we employed bioluminescence resonance energy transfer and isothermal titration calorimetry to show that BRD4 bromodomain binding of multiple acetylation sites on a histone tail does not increase BRD4-histone tail affinity, suggesting that BET bromodomain intranucleosome binding is not biologically relevant. Using sucrose gradients and amplified luminescent proximity homogeneous (AlphaScreen) assays, we provide the first direct biophysical evidence that BET bromodomains can scaffold multiple acetylated nucleosomes. Taken together, our results demonstrate that BET bromodomains are capable of multivalent internucleosome scaffolding in vitro. The knowledge gained provides implications for how BET bromodomain-mediated acetylated internucleosome scaffolding may maintain cellular chromatin interactions in active genetic regions.

Nucleosome Spacing Can Fine-Tune Higher Order Chromatin Assembly

Cellular chromatin displays heterogeneous structure and dynamics, properties that control diverse nuclear processes. Models invoke phase separation of conformational ensembles of chromatin fibers as a mechanism regulating chromatin organization in vivo. Here we combine biochemistry and molecular dynamics simulations to examine, at single base-pair resolution, how nucleosome spacing controls chromatin phase separation. We show that as DNA linkers extend from 25 bp to 30 bp, as examplars of 10N+5 and 10N (integer N) bp lengths, chromatin condensates become less thermodynamically stable and nucleosome mobility increases. Simulations reveal that this is due to trade-offs between inter- and intramolecular nucleosome stacking, favored by rigid 10N+5 and 10N bp linkers, respectively. A remodeler can induce or inhibit phase separation by moving nucleosomes, changing the balance between intra- and intermolecular stacking. The intrinsic phase separation capacity of chromatin enables fine tuning of compaction and dynamics, likely contributing to heterogeneous chromatin organization in vivo.

Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome

Motivation: We present a user-friendly 3D chromatin simulation model for the human genome based on OpenMM, addressing the challenges posed by existing models with use-specific implementations. Our approach employs a multi-scale energy minimization strategy, capturing chromatin's hierarchical structure. Initiating with a Hilbert curve-based structure, users can input files specifying nucleosome positioning, loops, compartments, or subcompartments. Results: The model utilizes an energy minimization approach with a large choice of numerical integrators, providing the entire genome's structure within minutes. Output files include the generated structures for each chromosome, offering a versatile and accessible tool for chromatin simulation in bioinformatics studies. Furthermore, MultiMM is capable of producing nucleosome-resolution structures by making simplistic geometric assumptions about the structure and the density of nucleosomes on the DNA. Code availability: Open-source software and the manual are freely available on https://github.com/SFGLab/MultiMM or via pip https://pypi.org/project/MultiMM/.

The chromosome folding problem and how cells solve it

Every cell must solve the problem of how to fold its genome. We describe how the folded state of chromosomes is the result of the combined activity of multiple conserved mechanisms. Homotypic affinity-driven interactions lead to spatial partitioning of active and inactive loci. Molecular motors fold chromosomes through loop extrusion. Topological features such as supercoiling and entanglements contribute to chromosome folding and its dynamics, and tethering loci to sub-nuclear structures adds additional constraints. Dramatically diverse chromosome conformations observed throughout the cell cycle and across the tree of life can be explained through differential regulation and implementation of these basic mechanisms. We propose that the first functions of chromosome folding are to mediate genome replication, compaction, and segregation and that mechanisms of folding have subsequently been co-opted for other roles, including long-range gene regulation, in different conditions, cell types, and species.

Structural dynamics and optimal transport of an active polymer

We study the spontaneous configuration transitions of an active semi-flexible polymer between spiral and non-spiral states, and show that the configuration dynamics is fully described by a subcritical pitchfork bifurcation. Exploiting the fact that an active polymer barely moves in spiral states and exhibits net displacements in non-spiral states, we theoretically prove that the motion of the active polymer is consistent with a run-and-tumble-like dynamics. Moreover, we find that there exists an optimal self-propelling force that maximizes the diffusion coefficient.

Multiplexed chromatin imaging reveals predominantly pairwise long-range coordination between Drosophila Polycomb genes

Polycomb (Pc) group proteins are transcriptional regulators with key roles in development, cell identity, and differentiation. Pc-bound chromatin regions form repressive domains that interact in 3D to assemble repressive nuclear compartments. Here, we use multiplexed chromatin imaging to investigate whether Pc compartments involve the clustering of multiple Pc domains during Drosophila development. Notably, 3D proximity between Pc targets is rare and involves predominantly pairwise interactions. These 3D proximities are particularly enhanced in segments where Pc genes are co-repressed. In addition, segment-specific expression of Hox Pc targets leads to their spatial segregation from Pc-repressed genes. Finally, non-Hox Pc targets are more proximal in regions where they are co-expressed. These results indicate that long-range Pc interactions are temporally and spatially regulated during differentiation and development but do not induce frequent clustering of multiple distant Pc genes.

Polycomb repression of Hox genes involves spatial feedback but not domain compaction or phase transition

Polycomb group proteins have a critical role in silencing transcription during development. It is commonly proposed that Polycomb-dependent changes in genome folding, which compact chromatin, contribute directly to repression by blocking the binding of activating complexes. Recently, it has also been argued that liquid-liquid demixing of Polycomb proteins facilitates this compaction and repression by phase-separating target genes into a membraneless compartment. To test these models, we used Optical Reconstruction of Chromatin Architecture to trace the Hoxa gene cluster, a canonical Polycomb target, in thousands of single cells. Across multiple cell types, we find that Polycomb-bound chromatin frequently explores decompact states and partial mixing with neighboring chromatin, while remaining uniformly repressed, challenging the repression-by-compaction or phase-separation models. Using polymer simulations, we show that these observed flexible ensembles can be explained by 'spatial feedback'-transient contacts that contribute to the propagation of the epigenetic state (epigenetic memory), without inducing a globular organization.

Computational methods for analysing multiscale 3D genome organization

Recent progress in whole-genome mapping and imaging technologies has enabled the characterization of the spatial organization and folding of the genome in the nucleus. In parallel, advanced computational methods have been developed to leverage these mapping data to reveal multiscale three-dimensional (3D) genome features and to provide a more complete view of genome structure and its connections to genome functions such as transcription. Here, we discuss how recently developed computational tools, including machine-learning-based methods and integrative structure-modelling frameworks, have led to a systematic, multiscale delineation of the connections among different scales of 3D genome organization, genomic and epigenomic features, functional nuclear components and genome function. However, approaches that more comprehensively integrate a wide variety of genomic and imaging datasets are still needed to uncover the functional role of 3D genome structure in defining cellular phenotypes in health and disease.

Interplay between epigenome and 3D chromatin structure

Epigenetic mechanisms, primarily mediated through histone and DNA modifications, play a pivotal role in orchestrating the functional identity of a cell and its response to environmental cues. Similarly, the spatial arrangement of chromatin within the threedimensional (3D) nucleus has been recognized as a significant factor influencing genomic function. Investigating the relationship between epigenetic regulation and 3D chromatin structure has revealed correlation and causality between these processes, from the global alignment of average chromatin structure with chromatin marks to the nuanced correlations at smaller scales. This review aims to dissect the biological significance and the interplay between the epigenome and 3D chromatin structure, while also exploring the underlying molecular mechanisms. By synthesizing insights from both experimental and modeling perspectives, we seek to provide a comprehensive understanding of cellular functions. [BMB Reports 2023; 56(12): 633-644].

Structure and dynamics of chemically active ring polymers: swelling to collapse

The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.

Epigenetic switching with asymmetric bridging interactions

Gene expression states are often stably sustained in cis despite massively disruptive events like DNA replication. This is achieved by on-going enzymatic activity that maintains parts of the DNA in either heterochromatic (packed) or euchromatic (free) states, each of which is stabilized by both positive feedback and bridging interactions between individual nucleosomes. In contrast to condensed matter, however, the dynamics is not only governed by equilibrium binding interactions but is also mediated by enzymes that recognize and act on specific amino acid tails of the nucleosomes. The mechanical result is that some nucleosomes can bind to one another and form tightly packed polymer configurations, whereas others remain unbound and form free, noncompact polymer configurations. Here, we study the consequences of such an asymmetric interaction pattern on the dynamics of epigenetic switching. We develop a 3D polymer model and show that traits associated with epigenetic switching, such as bistability and epigenetic memory, are permitted by such a model. We find, however, that the experimentally observed burst-like nature of some epigenetic switches is difficult to reproduce by this biologically motivated interaction. Instead, the behavior seen in experiments can be explained by introducing partial confinement, which particularly affects the euchromatic regions of the chromosome.

Strong interactions between highly dynamic lamina-associated domains and the nuclear envelope stabilize the 3D architecture of Drosophila interphase chromatin

BACKGROUND

Interactions among topologically associating domains (TADs), and between the nuclear envelope (NE) and lamina-associated domains (LADs) are expected to shape various aspects of three-dimensional (3D) chromatin structure and dynamics; however, relevant genome-wide experiments that may provide statistically significant conclusions remain difficult.

RESULTS

We have developed a coarse-grained dynamical model of D. melanogaster nuclei at TAD resolution that explicitly accounts for four distinct epigenetic classes of TADs and LAD-NE interactions. The model is parameterized to reproduce the experimental Hi-C map of the wild type (WT) nuclei; it describes time evolution of the chromatin over the G1 phase of the interphase. The simulations include an ensemble of nuclei, corresponding to the experimentally observed set of several possible mutual arrangements of chromosomal arms. The model is validated against multiple structural features of chromatin from several different experiments not used in model development. Predicted positioning of all LADs at the NE is highly dynamic-the same LAD can attach, detach and move far away from the NE multiple times during interphase. The probabilities of LADs to be in contact with the NE vary by an order of magnitude, despite all having the same affinity to the NE in the model. These probabilities are mostly determined by a highly variable local linear density of LADs along the genome, which also has the same strong effect on the predicted positioning of individual TADs -- higher probability of a TAD to be near NE is largely determined by a higher linear density of LADs surrounding this TAD. The distribution of LADs along the chromosome chains plays a notable role in maintaining a non-random average global structure of chromatin. Relatively high affinity of LADs to the NE in the WT nuclei substantially reduces sensitivity of the global radial chromatin distribution to variations in the strength of TAD-TAD interactions compared to the lamin depleted nuclei, where a small (0.5 kT) increase of cross-type TAD-TAD interactions doubles the chromatin density in the central nucleus region.

CONCLUSIONS

A dynamical model of the entire fruit fly genome makes multiple genome-wide predictions of biological interest. The distribution of LADs along the chromatin chains affects their probabilities to be in contact with the NE and radial positioning of highly mobile TADs, playing a notable role in creating a non-random average global structure of the chromatin. We conjecture that an important role of attractive LAD-NE interactions is to stabilize global chromatin structure against inevitable cell-to-cell variations in TAD-TAD interactions.

Phase transitions in heterochromatin organization

Heterochromatin formation has been proposed to involve phase transitions on the level of the three-dimensional folding of heterochromatin regions and the liquid-liquid demixing of heterochromatin proteins. Here, I outline the hallmarks of such transitions and the current challenges to detect them in living cells. I further discuss the abundance and properties of prominent heterochromatin proteins and relate them to their potential role in driving phase transitions. Recent data from mouse fibroblasts indicate that pericentric heterochromatin is organized via a reordering transition on the level of heterochromatin regions that does not necessarily involve liquid-liquid demixing of heterochromatin proteins. Evaluating key hallmarks of the different candidate phase transition mechanisms across cell types and species will be needed to complete the current picture.

4D epigenomics: deciphering the coupling between genome folding and epigenomic regulation with biophysical modeling

Recent experimental observations suggest a strong coupling between the 3D nuclear chromosome organization and epigenomics. However, the mechanistic and functional bases of such interplay remain elusive. In this review, we describe how biophysical modeling has been instrumental in characterizing how genome folding may impact the formation of epigenomic domains and, conversely, how epigenomic marks may affect chromosome conformation. Finally, we discuss how this mutual feedback loop between chromatin organization and epigenome regulation, via the formation of physicochemical nanoreactors, may represent a key functional role of 3D compartmentalization in the assembly and maintenance of stable - but yet plastic - epigenomic landscapes.

Dynamical modeling of the H3K27 epigenetic landscape in mouse embryonic stem cells

The Polycomb system via the methylation of the lysine 27 of histone H3 (H3K27) plays central roles in the silencing of many lineage-specific genes during development. Recent experimental evidence suggested that the recruitment of histone modifying enzymes like the Polycomb repressive complex 2 (PRC2) at specific sites and their spreading capacities from these sites are key to the establishment and maintenance of a proper epigenomic landscape around Polycomb-target genes. Here, to test whether such mechanisms, as a minimal set of qualitative rules, are quantitatively compatible with data, we developed a mathematical model that can predict the locus-specific distributions of H3K27 modifications based on previous biochemical knowledge. Within the biological context of mouse embryonic stem cells, our model showed quantitative agreement with experimental profiles of H3K27 acetylation and methylation around Polycomb-target genes in wild-type and mutants. In particular, we demonstrated the key role of the reader-writer module of PRC2 and of the competition between the binding of activating and repressing enzymes in shaping the H3K27 landscape around transcriptional start sites. The predicted dynamics of establishment and maintenance of the repressive trimethylated H3K27 state suggest a slow accumulation, in perfect agreement with experiments. Our approach represents a first step towards a quantitative description of PcG regulation in various cellular contexts and provides a generic framework to better characterize epigenetic regulation in normal or disease situations.

Painters in chromatin: a unified quantitative framework to systematically characterize epigenome regulation and memory

In eukaryotes, many stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of 'reader-writer' enzymes. In this work, we focus on the fundamental, generic mechanisms behind the epigenome memory encoded by post-translational modifications of histone tails. Based on experimental knowledge, we introduce a unified modeling framework, the painter model, describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader-writer processes and long-range spreading mechanisms. A systematic analysis of the model building blocks highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. The model also captures how chromatin state dynamics impact the intrinsic transcriptional properties of the region, slower kinetics leading to noisier expression. We finally apply our framework to analyze experimental data, from the propagation of γH2AX around DNA breaks in human cells to the maintenance of heterochromatin in fission yeast, illustrating how the painter model can be used to extract quantitative information on epigenomic molecular processes.

Uncovering the Principles of Genome Folding by 3D Chromatin Modeling

Our understanding of how genomic DNA is tightly packed inside the nucleus, yet is still accessible for vital cellular processes, has grown dramatically over recent years with advances in microscopy and genomics technologies. Computational methods have played a pivotal role in the structural interpretation of experimental data, which helped unravel some organizational principles of genome folding. Here, we give an overview of current computational efforts in mechanistic and data-driven 3D chromatin structure modeling. We discuss strengths and limitations of different methods and evaluate the added value and benefits of computational approaches to infer the 3D structural and dynamic properties of the genome and its underlying mechanisms at different scales and resolution, ranging from the dynamic formation of chromatin loops and topological associated domains to nuclear compartmentalization of chromatin and nuclear bodies.

A Liquid State Perspective on Dynamics of Chromatin Compartments

The interior of the eukaryotic cell nucleus has a crowded and heterogeneous environment packed with chromatin polymers, regulatory proteins, and RNA molecules. Chromatin polymer, assisted by epigenetic modifications, protein and RNA binders, forms multi-scale compartments which help regulate genes in response to cellular signals. Furthermore, chromatin compartments are dynamic and tend to evolve in size and composition in ways that are not fully understood. The latest super-resolution imaging experiments have revealed a much more dynamic and stochastic nature of chromatin compartments than was appreciated before. An emerging mechanism explaining chromatin compartmentalization dynamics is the phase separation of protein and nucleic acids into membraneless liquid condensates. Consequently, concepts and ideas from soft matter and polymer systems have been rapidly entering the lexicon of cell biology. In this respect, the role of computational models is crucial for establishing a rigorous and quantitative foundation for the new concepts and disentangling the complex interplay of forces that contribute to the emergent patterns of chromatin dynamics and organization. Several multi-scale models have emerged to address various aspects of chromatin dynamics, ranging from equilibrium polymer simulations, hybrid non-equilibrium simulations coupling protein binding and chromatin folding, and mesoscopic field-theoretic models. Here, we review these emerging theoretical paradigms and computational models with a particular focus on chromatin’s phase separation and liquid-like properties as a basis for nuclear organization and dynamics.

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

Current Understanding of Molecular Phase Separation in Chromosomes

Biomolecular phase separation denotes the demixing of a specific set of intracellular components without membrane encapsulation. Recent studies have found that biomolecular phase separation is involved in a wide range of cellular processes. In particular, phase separation is involved in the formation and regulation of chromosome structures at various levels. Here, we review the current understanding of biomolecular phase separation related to chromosomes. First, we discuss the fundamental principles of phase separation and introduce several examples of nuclear/chromosomal biomolecular assemblies formed by phase separation. We also briefly explain the experimental and computational methods used to study phase separation in chromosomes. Finally, we discuss a recent phase separation model, termed bridging-induced phase separation (BIPS), which can explain the formation of local chromosome structures.

Topological Constraints with Optimal Length Promote the Formation of Chromosomal Territories at Weakened Degree of Phase Separation

It is generally agreed that the nuclei of eukaryotic cells at interphase are partitioned into disjointed territories, with distinct regions occupied by certain chromosomes. However, the underlying mechanism for such territorialization is still under debate. Here we model chromosomes as coarse-grained block copolymers and to investigate the effect of loop domains (LDs) on the formation of compartments and territories based on dissipative particle dynamics. A critical length of LDs, which depends sensitively on the length of polymeric blocks, is obtained to minimize the degree of phase separation. This also applies to the two-polymer system: The critical length not only maximizes the degree of territorialization but also minimizes the degree of phase separation. Interestingly, by comparing with experimental data, we find the critical length for LDs and the corresponding length of blocks to be respectively very close to the mean length of topologically associating domains (TADs) and chromosomal segments with different densities of CpG islands for human chromosomes. The results indicate that topological constraints with optimal length can contribute to the formation of territories by weakening the degree of phase separation, which likely promotes the chromosomal flexibility in response to genetic regulations.

Generating Chromosome Geometries in a Minimal Cell From Cryo-Electron Tomograms and Chromosome Conformation Capture Maps

JCVI-syn3A is a genetically minimal bacterial cell, consisting of 493 genes and only a single 543 kbp circular chromosome. Syn3A’s genome and physical size are approximately one-tenth those of the model bacterial organism Escherichia coli’s, and the corresponding reduction in complexity and scale provides a unique opportunity for whole-cell modeling. Previous work established genome-scale gene essentiality and proteomics data along with its essential metabolic network and a kinetic model of genetic information processing. In addition to that information, whole-cell, spatially-resolved kinetic models require cellular architecture, including spatial distributions of ribosomes and the circular chromosome’s configuration. We reconstruct cellular architectures of Syn3A cells at the single-cell level directly from cryo-electron tomograms, including the ribosome distributions. We present a method of generating self-avoiding circular chromosome configurations in a lattice model with a resolution of 11.8 bp per monomer on a 4 nm cubic lattice. Realizations of the chromosome configurations are constrained by the ribosomes and geometry reconstructed from the tomograms and include DNA loops suggested by experimental chromosome conformation capture (3C) maps. Using ensembles of simulated chromosome configurations we predict chromosome contact maps for Syn3A cells at resolutions of 250 bp and greater and compare them to the experimental maps. Additionally, the spatial distributions of ribosomes and the DNA-crowding resulting from the individual chromosome configurations can be used to identify macromolecular structures formed from ribosomes and DNA, such as polysomes and expressomes.

Epigenomic landscape and 3D genome structure in pediatric high-grade glioma

Pediatric high-grade gliomas (pHGGs), including glioblastoma multiforme (GBM) and diffuse intrinsic pontine glioma (DIPG), are morbid brain tumors. Even with treatment survival is poor, making pHGG the number one cause of cancer death in children. Up to 80% of DIPGs harbor a somatic missense mutation in genes encoding histone H3. To investigate whether H3K27M is associated with distinct chromatin structure that alters transcription regulation, we generated the first high-resolution Hi-C maps of pHGG cell lines and tumor tissue. By integrating transcriptome (RNA-seq), enhancer landscape (ChIP-seq), genome structure (Hi-C), and chromatin accessibility (ATAC-seq) datasets from H3K27M and wild-type specimens, we identified tumor-specific enhancers and regulatory networks for known oncogenes. We identified genomic structural variations that lead to potential enhancer hijacking and gene coamplification, including A2M, JAG2, and FLRT1 Together, our results imply three-dimensional genome alterations may play a critical role in the pHGG epigenetic landscape and contribute to tumorigenesis.

Deciphering hierarchical organization of topologically associated domains through change-point testing

Background

The nucleus of eukaryotic cells spatially packages chromosomes into a hierarchical and distinct segregation that plays critical roles in maintaining transcription regulation. High-throughput methods of chromosome conformation capture, such as Hi-C, have revealed topologically associating domains (TADs) that are defined by biased chromatin interactions within them.

Results

We introduce a novel method, HiCKey, to decipher hierarchical TAD structures in Hi-C data and compare them across samples. We first derive a generalized likelihood-ratio (GLR) test for detecting change-points in an interaction matrix that follows a negative binomial distribution or general mixture distribution. We then employ several optimal search strategies to decipher hierarchical TADs with p values calculated by the GLR test. Large-scale validations of simulation data show that HiCKey has good precision in recalling known TADs and is robust against random collisions of chromatin interactions. By applying HiCKey to Hi-C data of seven human cell lines, we identified multiple layers of TAD organization among them, but the vast majority had no more than four layers. In particular, we found that TAD boundaries are significantly enriched in active chromosomal regions compared to repressed regions.

Conclusions

HiCKey is optimized for processing large matrices constructed from high-resolution Hi-C experiments. The method and theoretical result of the GLR test provide a general framework for significance testing of similar experimental chromatin interaction data that may not fully follow negative binomial distributions but rather more general mixture distributions.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04113-8.

Phase separation of DNA: From past to present

Phase separation of biological molecules, such as nucleic acids and proteins, has garnered widespread attention across many fields in recent years. For instance, liquid-liquid phase separation has been implicated not only in membraneless intracellular organization but also in many biochemical processes, including transcription, translation, and cellular signaling. Here, we present a historical background of biological phase separation and survey current work on nuclear organization and its connection to DNA phase separation from the perspective of DNA sequence, structure, and genomic context.

Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability

The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully understood, and current models often assume a long-range infectionlike process for the dynamics of marks, due to the polymeric nature of the chromatin fiber which allows looping between distant sites. While these existing models typically consider antagonizing marks, here we propose a qualitatively different scenario which analyses the spreading of a single mark. We define a one-dimensional stochastic model in which mark spreading/infection occurs as a long-range process whereas mark erasure/recovery is a local process, with an enhanced rate at boundaries of infected domains. In the limiting case where our model exhibits absorbing states, we find a first-order-like transition separating the marked/infected phase from the unmarked/recovered phase. This suggests that our model, in this limit, belongs to the long-range compact directed percolation universality class. The abrupt nature of the transition is retained in a more biophysically realistic situation when a basal infection/recovery rate is introduced (thereby removing absorbing states). Close to the transition there is a range of bistability where both the marked/infected and unmarked/recovered states are metastable and long lived, which provides a possible avenue for controlling fate decisions in cells. Increasing the basal infection/recovery rate, we find a second transition between a coherent (marked or unmarked) phase, and a mixed, or random, one.

Chromatin as an active polymeric material

The patterns of the large-scale spatial organization of chromatin in interphase human somatic cells are not random. Such patterns include the radial separation of euchromatin and heterochromatin, the territorial organization of individual chromosomes, the non-random locations of chromosome territories and the differential positioning of the two X chromosomes in female cells. These features of large-scale nuclear architecture follow naturally from the hypothesis that ATP-consuming non-equilibrium processes associated with highly transcribed regions of chromosomes are a source of 'active' forces. These forces are in excess of those that arise from Brownian motion. Simulations of model chromosomes that incorporate such activity recapitulate these features. In addition, they reproduce many other aspects of the spatial organization of chromatin at large scales that are known from experiments. Our results, reviewed here, suggest that the distribution of transcriptional activity across chromosomes underlies many aspects of large-scale nuclear architecture that were hitherto believed to be unrelated.

Mechanisms and Functions of Chromosome Compartmentalization

Active and inactive chromatin are spatially separated in the nucleus. In Hi-C data, this is reflected by the formation of compartments, whose interactions form a characteristic checkerboard pattern in chromatin interaction maps. Only recently have the mechanisms that drive this separation come into view. Here, we discuss new insights into these mechanisms and possible functions in genome regulation. Compartmentalization can be understood as a microphase-segregated block co-polymer. Microphase separation can be facilitated by chromatin factors that associate with compartment domains, and that can engage in liquid-liquid phase separation to form subnuclear bodies, as well as by acting as bridging factors between polymer sections. We then discuss how a spatially segregated state of the genome can contribute to gene regulation, and highlight experimental challenges for testing these structure-function relationships.

Hi-D: nanoscale mapping of nuclear dynamics in single living cells

Bulk chromatin motion has not been analyzed at high resolution. We present Hi-D, a method to quantitatively map dynamics of chromatin and abundant nuclear proteins for every pixel simultaneously over the entire nucleus from fluorescence image series. Hi-D combines reconstruction of chromatin motion and classification of local diffusion processes by Bayesian inference. We show that DNA dynamics in the nuclear interior are spatially partitioned into 0.3-3-μm domains in a mosaic-like pattern, uncoupled from chromatin compaction. This pattern was remodeled in response to transcriptional activity. Hi-D can be applied to any dense and bulk structures opening new perspectives towards understanding motion of nuclear molecules.

Single cell analysis pushes the boundaries of TAD formation and function

Eukaryotic genomes encode genetic information in their linear sequence, but appropriate expression of their genes requires chromosomes to fold into complex three-dimensional structures. Fueled by a growing collection of sequencing and imaging-based technologies, studies have uncovered a hierarchy of DNA interactions, from small chromatin loops that connect genes and enhancers to larger topologically associated domains (TADs) and compartments. However, despite the remarkable conservation of these organizational features, we have a very limited understanding of how this organization influences gene expression. This issue is further complicated in the context of single-cell heterogeneity, as has recently been revealed at both the level of gene activation and chromatin topology. Here, we provide a perspective on recent studies that address cell-to-cell variability and the relationship between structural heterogeneity and gene expression. We propose that transcription is regulated by variable 3D structures driven by at least two independent and partially redundant mechanisms. Collectively, this may provide flexibility to transcriptional regulation at the level of individual cells as well as reproducibility across whole tissues.

Pericentromeric heterochromatin is hierarchically organized and spatially contacts H3K9me2 islands in euchromatin

Membraneless pericentromeric heterochromatin (PCH) domains play vital roles in chromosome dynamics and genome stability. However, our current understanding of 3D genome organization does not include PCH domains because of technical challenges associated with repetitive sequences enriched in PCH genomic regions. We investigated the 3D architecture of Drosophila melanogaster PCH domains and their spatial associations with the euchromatic genome by developing a novel analysis method that incorporates genome-wide Hi-C reads originating from PCH DNA. Combined with cytogenetic analysis, we reveal a hierarchical organization of the PCH domains into distinct “territories.” Strikingly, H3K9me2-enriched regions embedded in the euchromatic genome show prevalent 3D interactions with the PCH domain. These spatial contacts require H3K9me2 enrichment, are likely mediated by liquid-liquid phase separation, and may influence organismal fitness. Our findings have important implications for how PCH architecture influences the function and evolution of both repetitive heterochromatin and the gene-rich euchromatin.

The three dimensional (3D) organization of genomes in cell nuclei can influence a wide variety of genome functions. However, most of our understanding of this critical architecture has been limited to the gene-rich euchromatin, and largely ignores the gene-poor and repeat-rich pericentromeric heterochromatin, or PCH. PCH comprises a large part of most eukaryotic genomes, forms 3D membraneless PCH domains in nuclei, and plays a vital role in chromosome dynamics and genome stability. In this study, we developed a new method that overcomes the technical challenges imposed by the highly repetitive PCH DNA, and generated a comprehensive picture of its 3D organization. Combined with image analyses, we reveal a hierarchical organization of the PCH domains. Surprisingly, we showed that distant euchromatic regions enriched for repressive epigenetic marks also dynamically interact with the main PCH domains. These 3D interactions are likely mediated by liquid-liquid phase separation (similar to how oil and vinegar separate in salad dressing) and the resulting liquid-like fusion events, and can influence the fitness of individuals. Our discoveries have strong implications for how seemingly “junk” DNA could impact functions in the gene-rich euchromatin.

Role of nucleosome positioning in 3D chromatin organization and loop formation

We present a physics-based polymer model that can investigate 3D organization of chromatin accounting for DNA elasticity, DNA-bending due to nucleosomes, and 1D organization of nucleosomes along DNA. We find that the packing density of chromatin oscillates between densities corresponding to highly folded and extended configurations as we change the nucleosome organization (length of linker DNA). We compute the looping probability of chromatin and show that the presence of nucleosomes increases the looping probability of the chain compared to that of a bare DNA. We also show that looping probability has a large variability depending on the nature of nucleosome organization and density of linker histones.

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

Understanding the spatial organization of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical-or epigenetic-marks that are deposited along the genome are thought to play an important, yet poorly understood, role in determining genome organization and cell identity. The physical principles underlying the interplay between epigenetic dynamics and genome folding remain elusive. Here we propose and study a theory that assumes a coupling between epigenetic mark and genome densities, and which can be applied at the scale of the whole nucleus. We show that equilibrium models are not compatible with experiments and a qualitative agreement is recovered by accounting for nonequilibrium processes that can stabilize microphase separated epigenomic domains. We finally discuss the potential biophysical origin of these terms.

Nonequilibrium Biophysical Processes Influence the Large-Scale Architecture of the Cell Nucleus

Model approaches to nuclear architecture have traditionally ignored the biophysical consequences of ATP-fueled active processes acting on chromatin. However, transcription-coupled activity is a source of stochastic forces that are substantially larger than the Brownian forces present at physiological temperatures. Here, we describe an approach to large-scale nuclear architecture in metazoans that incorporates cell-type-specific active processes. The model predicts the statistics of positional distributions, shapes, and overlaps of each chromosome. Simulations of the model reproduce common organizing principles underlying large-scale nuclear architecture across human cell nuclei in interphase. These include the differential positioning of euchromatin and heterochromatin, the territorial organization of chromosomes (including both gene-density-based and size-based chromosome radial positioning schemes), the nonrandom locations of chromosome territories, and the shape statistics of individual chromosomes. We propose that the biophysical consequences of the distribution of transcriptional activity across chromosomes should be central to any chromosome positioning code.

Magnetic polymer models for epigenetics-driven chromosome folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Opposite to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes-and hence on the expression of the underlying genes-by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for nonequilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

Bridging chromatin structure and function over a range of experimental spatial and temporal scales by molecular modeling

Chromatin structure, dynamics, and function are being intensely investigated by a variety of methods, including microscopy, X-ray diffraction, nuclear magnetic resonance, biochemical crosslinking, chromosome conformation capture, and computation. A range of experimental techniques combined with modeling is clearly valuable to help interpret experimental data and, importantly, generate configurations and mechanisms related to the 3D organization and function of the genome. Contact maps, in particular, as obtained by a variety of chromosome conformation capture methods, are of increasing interest due to their implications on genome structure and regulation on many levels. In this perspective, using seven examples from our group's studies, we illustrate how molecular modeling can help interpret such experimental data. Specifically, we show how computed contact maps related to experimental systems can be used to explain structures of nucleosomes, chromatin higher-order folding, domain segregation mechanisms, gene organization, and the effect on chromatin structure of external and internal fiber parameters, such as nucleosome positioning, presence of nucleosome free regions, histone posttranslational modifications, and linker histone binding. We argue that such computations on multiple spatial and temporal scales will be increasingly important for the integration of genomic, epigenomic, and biophysical data on chromatin structure and related cellular processes.

Transcription-driven genome organization: a model for chromosome structure and the regulation of gene expression tested through simulations

Current models for the folding of the human genome see a hierarchy stretching down from chromosome territories, through A/B compartments and topologically-associating domains (TADs), to contact domains stabilized by cohesin and CTCF. However, molecular mechanisms underlying this folding, and the way folding affects transcriptional activity, remain obscure. Here we review physical principles driving proteins bound to long polymers into clusters surrounded by loops, and present a parsimonious yet comprehensive model for the way the organization determines function. We argue that clusters of active RNA polymerases and their transcription factors are major architectural features; then, contact domains, TADs and compartments just reflect one or more loops and clusters. We suggest tethering a gene close to a cluster containing appropriate factors—a transcription factory—increases the firing frequency, and offer solutions to many current puzzles concerning the actions of enhancers, super-enhancers, boundaries and eQTLs (expression quantitative trait loci). As a result, the activity of any gene is directly influenced by the activity of other transcription units around it in 3D space, and this is supported by Brownian-dynamics simulations of transcription factors binding to cognate sites on long polymers.

Epigenomics in 3D: importance of long-range spreading and specific interactions in epigenomic maintenance

Recent progresses of genome-wide chromatin conformation capture techniques have shown that the genome is segmented into hierarchically organized spatial compartments. However, whether this non-random 3D organization only reflects or indeed contributes—and how—to the regulation of genome function remain to be elucidated. The observation in many species that 3D domains correlate strongly with the 1D epigenomic information along the genome suggests a dynamic coupling between chromatin organization and epigenetic regulation. Here, we posit that chromosome folding may contribute to the maintenance of a robust epigenomic identity via the formation of spatial compartments like topologically-associating domains. Using a novel theoretical framework, the living chromatin model, we show that 3D compartmentalization leads to the spatial colocalization of epigenome regulators, thus increasing their local concentration and enhancing their ability to spread an epigenomic signal at long-range. Interestingly, we find that the presence of 1D insulator elements, like CTCF, may contribute greatly to the stable maintenance of adjacent antagonistic epigenomic domains. We discuss the generic implications of our findings in the light of various biological contexts from yeast to human. Our approach provides a modular framework to improve our understanding and to investigate in details the coupling between the structure and function of chromatin.

Two major mechanisms of chromosome organization

The spatial organization of chromosomes has long been connected to their polymeric nature and is believed to be important for their biological functions, including the control of interactions between genomic elements, the maintenance of genetic information, and the compaction and safe transfer of chromosomes to cellular progeny. chromosome conformation capture techniques, particularly Hi-C, have provided a comprehensive picture of spatial chromosome organization and revealed new features and elements of chromosome folding. Furthermore, recent advances in microscopy have made it possible to obtain distance maps for extensive regions of chromosomes (Bintu et al., 2018; Nir et al., 2018 [2^••,3]), providing information complementary to, and in excellent agreement with, Hi-C maps. Not only has the resolution of both techniques advanced significantly, but new perturbation data generated in the last two years have led to the identification of molecular mechanisms behind large-scale genome organization. Two major mechanisms that have been proposed to govern chromosome organization are (i) the active (ATP-dependent) process of loop extrusion by Structural Maintenance of Chromosomes (SMC) complexes, and (ii) the spatial compartmentalization of the genome, which is likely mediated by affinity interactions between heterochromatic regions (Falk et al., 2019 [76^••]) rather than by ATP-dependent processes. Here, we review existing evidence that these two processes operate together to fold chromosomes in interphase and that loop extrusion alone drives mitotic compaction. We discuss possible implications of these mechanisms for chromosome function.

Polymer coil-globule phase transition is a universal folding principle of Drosophila epigenetic domains

Background

Localized functional domains within chromosomes, known as topologically associating domains (TADs), have been recently highlighted. In Drosophila, TADs are biochemically defined by epigenetic marks, this suggesting that the 3D arrangement may be the “missing link” between epigenetics and gene activity. Recent observations (Boettiger et al. in Nature 529(7586):418–422, 2016) provide access to structural features of these domains with unprecedented resolution thanks to super-resolution experiments. In particular, they give access to the distribution of the radii of gyration for domains of different linear length and associated with different transcriptional activity states: active, inactive or repressed. Intriguingly, the observed scaling laws lack consistent interpretation in polymer physics.

Results

We develop a new methodology conceived to extract the best information from such super-resolution data by exploiting the whole distribution of gyration radii, and to place these experimental results on a theoretical framework. We show that the experimental data are compatible with the finite-size behavior of a self-attracting polymer. The same generic polymer model leads to quantitative differences between active, inactive and repressed domains. Active domains behave as pure polymer coils, while inactive and repressed domains both lie at the coil–globule crossover. For the first time, the “color-specificity” of both the persistence length and the mean interaction energy are estimated, leading to important differences between epigenetic states.

Conclusion

These results point toward a crucial role of criticality to enhance the system responsivity, resulting in both energy transitions and structural rearrangements. We get strong indications that epigenetically induced changes in nucleosome–nucleosome interaction can cause chromatin to shift between different activity states.

Electronic supplementary material

The online version of this article (10.1186/s13072-019-0269-6) contains supplementary material, which is available to authorized users.

Physical principles and functional consequences of nuclear compartmentalization in budding yeast

One striking feature of eukaryotic nuclei is the existence of discrete regions, in which specific factors concentrate while others are excluded, thus forming microenvironments with different molecular compositions and biological functions. These domains are often referred to as subcompartments even though they are not membrane enclosed. Despite their functional importance the physical nature of these structures remains largely unknown. Here, we describe how the Saccharomyces cerevisiae nucleus is compartmentalized and discuss possible physical models underlying the formation and maintenance of chromatin associated subcompartments. Focusing on three particular examples, the nucleolus, silencing foci, and repair foci, we discuss the biological implications of these different models as well as possible approaches to challenge them in living cells.

Organizational principles of 3D genome architecture

Studies of 3D chromatin organization have suggested that chromosomes are hierarchically organized into large compartments composed of smaller domains called topologically associating domains (TADs). Recent evidence suggests that compartments are smaller than previously thought and that the transcriptional or chromatin state is responsible for interactions leading to the formation of small compartmental domains in all organisms. In vertebrates, CTCF forms loop domains, probably via an extrusion process involving cohesin. CTCF loops cooperate with compartmental domains to establish the 3D organization of the genome. The continuous extrusion of the chromatin fibre by cohesin may also be responsible for the establishment of enhancer-promoter interactions and stochastic aspects of the transcription process. These observations suggest that the 3D organization of the genome is an emergent property of chromatin and its components, and thus may not be only a determinant but also a consequence of its function.

Phase separated microenvironments inside the cell nucleus are linked to disease and regulate epigenetic state, transcription and RNA processing

Proteins and RNAs inside the cell nucleus are organized into distinct phases, also known as liquid-liquid phase separated (LLPS) droplet organelles or nuclear bodies. These regions exist within the spaces between chromatin-rich regions but their function is tightly linked to gene activity. They include major microscopically-observable structures such as the nucleolus, paraspeckle and Cajal body. The biochemical and assembly factors enriched inside these microenvironments regulate chromatin structure, transcription, and RNA processing, and other important cellular functions. Here, we describe published evidence that suggests nuclear bodies are bona fide LLPS droplet organelles and major regulators of the processes listed above. We also outline an updated "Supply or Sequester" model to describe nuclear body function, in which proteins or RNAs are supplied to surrounding genomic regions or sequestered away from their sites of activity. Finally, we describe recent evidence that suggests these microenvironments are both reflective and drivers of diverse pathophysiological states.

Molecular mechanisms driving transcriptional stress responses

Proteotoxic stress, that is, stress caused by protein misfolding and aggregation, triggers the rapid and global reprogramming of transcription at genes and enhancers. Genome-wide assays that track transcriptionally engaged RNA polymerase II (Pol II) at nucleotide resolution have provided key insights into the underlying molecular mechanisms that regulate transcriptional responses to stress. In addition, recent kinetic analyses of transcriptional control under heat stress have shown how cells 'prewire' and rapidly execute genome-wide changes in transcription while concurrently becoming poised for recovery. The regulation of Pol II at genes and enhancers in response to heat stress is coupled to chromatin modification and compartmentalization, as well as to co-transcriptional RNA processing. These mechanistic features seem to apply broadly to other coordinated genome-regulatory responses.

How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes

The 3D organization of chromosomes is crucial for regulating gene expression and cell function. Many experimental and polymer modeling efforts are dedicated to deciphering the mechanistic principles behind chromosome folding. Chromosomes are long and densely packed-topologically constrained-polymers. The main challenges are therefore to develop adequate models and simulation methods to investigate properly the multi spatio-temporal scales of such macromolecules. Here, we proposed a generic strategy to develop efficient coarse-grained models for self-avoiding polymers on a lattice. Accounting accurately for the polymer entanglement length and the volumic density, we show that our simulation scheme not only captures the steady-state structural and dynamical properties of the system but also tracks the same dynamics at different coarse-graining. This strategy allows a strong power-law gain in numerical efficiency and offers a systematic way to define reliable coarse-grained null models for chromosomes and to go beyond the current limitations by studying long chromosomes during an extended time period with good statistics. We use our formalism to investigate in details the time evolution of the 3D organization of chromosome 3R (20 Mbp) in drosophila during one cell cycle (20 hours). We show that a combination of our coarse-graining strategy with a one-parameter block copolymer model integrating epigenomic-driven interactions quantitatively reproduce experimental data at the chromosome-scale and predict that chromatin motion is very dynamic during the cell cycle.

Real-Time Imaging of a Single Gene Reveals Transcription-Initiated Local Confinement

Genome dynamics are intimately linked to the regulation of gene expression, the most fundamental mechanism in biology, yet we still do not know whether the very process of transcription drives spatial organization at specific gene loci. Here, we have optimized the ANCHOR/ParB DNA-labeling system for real-time imaging of a single-copy, estrogen-inducible transgene in human cells. Motion of an ANCHOR3-tagged DNA locus was recorded in the same cell before and during the appearance of nascent MS2-labeled mRNA. We found that transcription initiation by RNA polymerase 2 resulted in confinement of the mRNA-producing gene domain within minutes. Transcription-induced confinement occurred in each single cell independently of initial, highly heterogeneous mobility. Constrained mobility was maintained even when inhibiting polymerase elongation. Chromatin motion at constant step size within a largely confined area hence leads to increased collisions that are compatible with the formation of gene-specific chromatin domains, and reflect the assembly of functional protein hubs and DNA processing during the rate-limiting steps of transcription.