Predicting the three-dimensional folding of cis-regulatory regions in mammalian genomes using bioinformatic data and polymer models

Multiscale Bayesian simulations reveal functional chromatin condensation of gene loci

Chromatin, the complex assembly of DNA and associated proteins, plays a pivotal role in orchestrating various genomic functions. To aid our understanding of the principles underlying chromatin organization, we introduce Hi-C metainference, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin. This approach combines both bottom-up (the physics-based prior) and top-down (the data-driven posterior) strategies to characterize the 3D organization of a target genomic locus. We first demonstrate the capability of this method to accurately reconstruct the structural ensemble and the dynamics of a system from contact information. We then apply the approach to investigate the Sox2, Pou5f1, and Nanog loci of mouse embryonic stem cells using a bottom-up chromatin model at 1 kb resolution. We observe that the studied loci are conformationally heterogeneous and organized as crumpled globules, favoring contacts between distant enhancers and promoters. Using nucleosome-resolution simulations, we then reveal how the Nanog gene is functionally organized across the multiple scales of chromatin. At the local level, we identify diverse tetranucleosome folding motifs with a characteristic distribution along the genome, predominantly open at cis-regulatory elements and compact in between. At the larger scale, we find that enhancer-promoter contacts are driven by the transient condensation of chromatin into compact domains stabilized by extensive internucleosome interactions. Overall, this work highlights the condensed, but dynamic nature of chromatin in vivo, contributing to a deeper understanding of gene structure-function relationships.

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.

Chromatin structure from high resolution microscopy: Scaling laws and microphase separation

Recent advances in experimental fluorescence microscopy allow high accuracy determination (resolution of 50 nm) of the three-dimensional physical location of multiple (up to ∼10^{2}) tagged regions of the chromosome. We investigate publicly available microscopy data for two loci of the human Chr21 obtained from multiplexed fluorescence in situ hybridization (FISH) methods for different cell lines and treatments. Inspired by polymer physics models, our analysis centers around distance distributions between different tags with the aim being to unravel the chromatin conformational arrangements. We show that for any specific genomic site, there are (at least) two different conformational arrangements of chromatin, implying coexisting distinct topologies which we refer to as phase α and phase β. These two phases show different scaling behaviors: the former is consistent with a crumpled globule, while the latter indicates a confined, but more extended conformation, such as a looped domain. The identification of these distinct phases sheds light on the coexistence of multiple chromatin topologies and provides insights into the effects of cellular context and/or treatments on chromatin structure.

Effective modeling of the chromatin structure by coarse-grained methods

The interphase chromatin structure is extremely complex, precise and dynamic. Experimental methods can only show the frequency of interaction of the various parts of the chromatin. Therefore, it is extremely important to develop theoretical methods to predict the chromatin structure. In this publication, we implemented an extended version of the SBS model described by Barbieri et al. and created the ChroMC program that is easy to use and freely available (https://github.com/regulomics/chroMC) to other users. We also describe the necessary factors for the effective modeling of the chromatin structure in Drosophila melanogaster. We compared results of chromatin structure predictions using two methods: Monte Carlo and Molecular Dynamic. Our simulations suggest that incorporating black, non-reactive chromatin is necessary for successful prediction of chromatin structure, while the loop extrusion model with a long range attraction potential or Lennard-Jones (with local attraction force) as well as using Hi-C data as input are not essential for the basic structure reconstruction. We also proposed a new way to calculate the similarity of the properties of contact maps including the calculation of local similarity.Communicated by Ramaswamy H. Sarma.

Transcription modulates chromatin dynamics and locus configuration sampling

In living cells, the 3D structure of gene loci is dynamic, but this is not revealed by 3C and FISH experiments in fixed samples, leaving a notable gap in our understanding. To overcome these limitations, we applied the highly predictive heteromorphic polymer (HiP-HoP) model to determine chromatin fiber mobility at the Pax6 locus in three mouse cell lines with different transcription states. While transcriptional activity minimally affects movement of 40-kbp regions, we observed that motion of smaller 1-kbp regions depends strongly on local disruption to chromatin fiber structure marked by H3K27 acetylation. This also substantially influenced locus configuration dynamics by modulating protein-mediated promoter-enhancer loops. Importantly, these simulations indicate that chromatin dynamics are sufficiently fast to sample all possible locus conformations within minutes, generating wide dynamic variability within single cells. This combination of simulation and experimental validation provides insight into how transcriptional activity influences chromatin structure and gene dynamics.

Predicting scale-dependent chromatin polymer properties from systematic coarse-graining

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations.

Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide.

MINE is a method for detecting spatial density of regulatory chromatin interactions based on a multi-modal network

Chromatin interactions play essential roles in chromatin conformation and gene expression. However, few tools exist to analyze the spatial density of regulatory chromatin interactions (SD-RCI). Here, we present the multi-modal network (MINE) toolkit, including MINE-Loop, MINE-Density, and MINE-Viewer. The MINE-Loop network aims to enhance the detection of RCIs, MINE-Density quantifies the SD--RCI, and MINE-Viewer facilitates 3D visualization of the density of chromatin interactions and participating regulatory factors (e.g., transcription factors). We applied MINE to investigate the relationship between the SD-RCI and chromatin volume change in HeLa cells before and after liquid-liquid phase separation. Changes in SD-RCI before and after treating the HeLa cells with 1,6-hexanediol suggest that changes in chromatin organization was related to the degree of activation or repression of genes. Together, the MINE toolkit enables quantitative studies on different aspects of chromatin conformation and regulatory activity.

Interphase chromosomes of the Aedes aegypti mosquito are liquid crystalline and can sense mechanical cues

We use data-driven physical simulations to study the three-dimensional architecture of the Aedes aegypti genome. Hi-C maps exhibit both a broad diagonal and compartmentalization with telomeres and centromeres clustering together. Physical modeling reveals that these observations correspond to an ensemble of 3D chromosomal structures that are folded over and partially condensed. Clustering of the centromeres and telomeres near the nuclear lamina appears to be a necessary condition for the formation of the observed structures. Further analysis of the mechanical properties of the genome reveals that the chromosomes of Aedes aegypti, by virtue of their atypical structural organization, are highly sensitive to the deformation of the nuclei. This last finding provides a possible physical mechanism linking mechanical cues to gene regulation.

The dynamics of three-dimensional chromatin organization and phase separation in cell fate transitions and diseases

Cell fate transition is a fascinating process involving complex dynamics of three-dimensional (3D) chromatin organization and phase separation, which play an essential role in cell fate decision by regulating gene expression. Phase separation is increasingly being considered a driving force of chromatin folding. In this review, we have summarized the dynamic features of 3D chromatin and phase separation during physiological and pathological cell fate transitions and systematically analyzed recent evidence of phase separation facilitating the chromatin structure. In addition, we discuss current advances in understanding how phase separation contributes to physical and functional enhancer-promoter contacts. We highlight the functional roles of 3D chromatin organization and phase separation in cell fate transitions, and more explorations are required to study the regulatory relationship between 3D chromatin organization and phase separation. 3D chromatin organization (shown by Hi-C contact map) and phase separation are highly dynamic and play functional roles during early embryonic development, cell differentiation, somatic reprogramming, cell transdifferentiation and pathogenetic process. Phase separation can regulate 3D chromatin organization directly, but whether 3D chromatin organization regulates phase separation remains unclear.

High-resolution simulations of chromatin folding at genomic rearrangements in malignant B cells provide mechanistic insights into proto-oncogene deregulation

Genomic rearrangements are known to result in proto-oncogene deregulation in many cancers, but the link to 3D genome structure remains poorly understood. Here, we used the highly predictive heteromorphic polymer (HiP-HoP) model to predict chromatin conformations at the proto-oncogene CCND1 in healthy and malignant B cells. After confirming that the model gives good predictions of Hi-C data for the nonmalignant human B cell-derived cell line GM12878, we generated predictions for two cancer cell lines, U266 and Z-138. These possess genome rearrangements involving CCND1 and the immunoglobulin heavy locus (IGH), which we mapped using targeted genome sequencing. Our simulations showed that a rearrangement in U266 cells where a single IGH super-enhancer is inserted next to CCND1 leaves the local topologically associated domain (TAD) structure intact. We also observed extensive changes in enhancer-promoter interactions within the TAD, suggesting that it is the downstream chromatin remodeling which gives rise to the oncogene activation, rather than the presence of the inserted super-enhancer DNA sequence per se. Simulations of the IGH-CCND1 reciprocal translocation in Z-138 cells revealed that an oncogenic fusion TAD is created, encompassing CCND1 and the IGH super-enhancers. We predicted how the structure and expression of CCND1 changes in these different cell lines, validating this using qPCR and fluorescence in situ hybridization microscopy. Our work demonstrates the power of polymer simulations to predict differences in chromatin interactions and gene expression for different translocation breakpoints.

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation, and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction-strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its three-dimensional organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid- and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.

Loop-extrusion and polymer phase-separation can co-exist at the single-molecule level to shape chromatin folding

Loop-extrusion and phase-separation have been proposed as mechanisms that shape chromosome spatial organization. It is unclear, however, how they perform relative to each other in explaining chromatin architecture data and whether they compete or co-exist at the single-molecule level. Here, we compare models of polymer physics based on loop-extrusion and phase-separation, as well as models where both mechanisms act simultaneously in a single molecule, against multiplexed FISH data available in human loci in IMR90 and HCT116 cells. We find that the different models recapitulate bulk Hi-C and average multiplexed microscopy data. Single-molecule chromatin conformations are also well captured, especially by phase-separation based models that better reflect the experimentally reported segregation in globules of the considered genomic loci and their cell-to-cell structural variability. Such a variability is consistent with two main concurrent causes: single-cell epigenetic heterogeneity and an intrinsic thermodynamic conformational degeneracy of folding. Overall, the model combining loop-extrusion and polymer phase-separation provides a very good description of the data, particularly higher-order contacts, showing that the two mechanisms can co-exist in shaping chromatin architecture in single cells.

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.

Reconstruct high-resolution 3D genome structures for diverse cell-types using FLAMINGO

High-resolution reconstruction of spatial chromosome organizations from chromatin contact maps is highly demanded, but is hindered by extensive pairwise constraints, substantial missing data, and limited resolution and cell-type availabilities. Here, we present FLAMINGO, a computational method that addresses these challenges by compressing inter-dependent Hi-C interactions to delineate the underlying low-rank structures in 3D space, based on the low-rank matrix completion technique. FLAMINGO successfully generates 5 kb- and 1 kb-resolution spatial conformations for all chromosomes in the human genome across multiple cell-types, the largest resources to date. Compared to other methods using various experimental metrics, FLAMINGO consistently demonstrates superior accuracy in recapitulating observed structures with raises in scalability by orders of magnitude. The reconstructed 3D structures efficiently facilitate discoveries of higher-order multi-way interactions, imply biological interpretations of long-range QTLs, reveal geometrical properties of chromatin, and provide high-resolution references to understand structural variabilities. Importantly, FLAMINGO achieves robust predictions against high rates of missing data and significantly boosts 3D structure resolutions. Moreover, FLAMINGO shows vigorous cross cell-type structure predictions that capture cell-type specific spatial configurations via integration of 1D epigenomic signals. FLAMINGO can be widely applied to large-scale chromatin contact maps and expand high-resolution spatial genome conformations for diverse cell-types.

High-resolution reconstruction of spatial chromosome organisation is in demand. Here the authors report FLAMINGO, for reconstructing high-resolution 3D Genome Organisation from HiC data which they use to generate both 5 kb and 1 kb-resolution 3D chromosomal structures for the human genome.

Polymer physics reveals a combinatorial code linking 3D chromatin architecture to 1D chromatin states

The mammalian genome has a complex, functional 3D organization. However, it remains largely unknown how DNA contacts are orchestrated by chromatin organizers. Here, we infer from only Hi-C the cell-type-specific arrangement of DNA binding sites sufficient to recapitulate, through polymer physics, contact patterns genome wide. Our model is validated by its predictions in a set of duplications at Sox9 against available independent data. The binding site types fall in classes that well match chromatin states from segmentation studies, yet they have an overlapping, combinatorial organization along chromosomes necessary to accurately explain contact specificity. The chromatin signatures of the binding site types return a code linking chromatin states to 3D architecture. The code is validated by extensive de novo predictions of Hi-C maps in an independent set of chromosomes. Overall, our results shed light on how 3D information is encrypted in 1D chromatin via the specific combinatorial arrangement of binding sites.

Dynamic and equilibrium properties of finite-size polymer models of chromosome folding

Novel technologies are revealing that chromosomes have a complex three-dimensional organization within the cell nucleus that serves functional purposes. Models from polymer physics have been developed to quantitively understand the molecular principles controlling their structure and folding mechanisms. Here, by using massive molecular-dynamics simulations we show that classical scaling laws combined with finite-size effects of a simple polymer model can effectively explain the scaling behavior that chromatin exhibits at the topologically associating domains level, as revealed by experimental observations. Model results are then validated against recently published high-resolution in situ Hi-C data.

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.

The interplay of chromatin phase separation and lamina interactions in nuclear organization

The genetic material of eukaryotes is segregated into transcriptionally active euchromatin and silent heterochromatin compartments. The spatial arrangement of chromatin compartments evolves over the course of cellular life in a process that remains poorly understood. The latest nuclear imaging experiments reveal a number of dynamical signatures of chromatin that are reminiscent of active multiphase liquids. This includes the observations of viscoelastic response, coherent motions, Ostwald ripening, and coalescence of chromatin compartments. There is also growing evidence that liquid-liquid phase separation of protein and nucleic acid components is the underlying mechanism for the dynamical behavior of chromatin. To dissect the organizational and dynamical implications of chromatin's liquid behavior, we have devised a phenomenological field-theoretic model of the nucleus as a multiphase condensate of liquid chromatin types. Employing the liquid chromatin model of the Drosophila nucleus, we have carried out an extensive set of simulations with an objective to shed light on the dynamics and chromatin patterning observed in the latest nuclear imaging experiments. Our simulations reveal the emergence of experimentally detected mesoscale chromatin channels and spheroidal droplets which arise from the dynamic interplay of chromatin type to type interactions and intermingling of chromosomal territories. We also quantitatively reproduce coherent motions of chromatin domains observed in displacement correlation spectroscopy measurements which are explained within the framework of our model by phase separation of chromatin types operating within constrained intrachromosomal and interchromosomal boundaries. Finally, we illuminate the role of heterochromatin-lamina interactions in the nuclear organization by showing that these interactions enhance the mobility of euchromatin and indirectly introduce correlated motions of heterochromatin droplets.

Polymer models are a versatile tool to study chromatin 3D organization

The development of new experimental technologies is opening the way to a deeper investigation of the three-dimensional organization of chromosomes inside the cell nucleus. Genome architecture is linked to vital functional purposes, yet a full comprehension of the mechanisms behind DNA folding is still far from being accomplished. Theoretical approaches based on polymer physics have been employed to understand the complexity of chromatin architecture data and to unveil the basic mechanisms shaping its structure. Here, we review some recent advances in the field to discuss how Polymer Physics, combined with numerical Molecular Dynamics simulation and Machine Learning based inference, can capture important aspects of genome organization, including the description of tissue-specific structural rearrangements, the detection of novel, regulatory-linked architectural elements and the structural variability of chromatin at the single-cell level.

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.

Nonequilibrium dynamics and action at a distance in transcriptionally driven DNA supercoiling

We study the effect of transcription on the kinetics of DNA supercoiling in three dimensions by means of Brownian dynamics simulations of a single-nucleotide-resolution coarse-grained model for double-stranded DNA. By explicitly accounting for the action of a transcribing RNA polymerase (RNAP), we characterize the geometry and nonequilibrium dynamics of the ensuing twin supercoiling domains. Contrary to the typical textbook picture, we find that the generation of twist by RNAP results in the formation of plectonemes (writhed DNA) some distance away. We further demonstrate that this translates into an "action at a distance" on DNA-binding proteins; for instance, positive supercoils downstream of an elongating RNAP destabilize nucleosomes long before the transcriptional machinery reaches the histone octamer. We also analyze the relaxation dynamics of supercoiled double-stranded DNA, and characterize the widely different timescales of twist diffusion, which is a simple and fast process, and writhe relaxation, which is much slower and entails multiple steps.

Polymer modelling unveils the roles of heterochromatin and nucleolar organizing regions in shaping 3D genome organization in Arabidopsis thaliana

The 3D genome is characterized by a complex organization made of genomic and epigenomic layers with profound implications on gene regulation and cell function. However, the understanding of the fundamental mechanisms driving the crosstalk between nuclear architecture and (epi)genomic information is still lacking. The plant Arabidopsis thaliana is a powerful model organism to address these questions owing to its compact genome for which we have a rich collection of microscopy, chromosome conformation capture (Hi-C) and ChIP-seq experiments. Using polymer modelling, we investigate the roles of nucleolus formation and epigenomics-driven interactions in shaping the 3D genome of A. thaliana. By validation of several predictions with published data, we demonstrate that self-attracting nucleolar organizing regions and repulsive constitutive heterochromatin are major mechanisms to regulate the organization of chromosomes. Simulations also suggest that interphase chromosomes maintain a partial structural memory of the V-shapes, typical of (sub)metacentric chromosomes in anaphase. Additionally, self-attraction between facultative heterochromatin regions facilitates the formation of Polycomb bodies hosting H3K27me3-enriched gene-clusters. Since nucleolus and heterochromatin are highly-conserved in eukaryotic cells, our findings pave the way for a comprehensive characterization of the generic principles that are likely to shape and regulate the 3D genome in many species.

A DNA Sequence Based Polymer Model for Chromatin Folding

The recent development of sequencing technology and imaging methods has provided an unprecedented understanding of the inter-phase chromatin folding in mammalian nuclei. It was found that chromatin folds into topological-associated domains (TADs) of hundreds of kilo base pairs (kbps), and is further divided into spatially segregated compartments (A and B). The compartment B tends to be located near to the periphery or the nuclear center and interacts with other domains of compartments B, while compartment A tends to be located between compartment B and interacts inside the domains. These spatial domains are found to highly correlate with the mosaic CpG island (CGI) density. High CGI density corresponds to compartments A and small TADs, and vice versa. The variation of contact probability as a function of sequential distance roughly follows a power-law decay. Different chromosomes tend to segregate to occupy different chromosome territories. A model that can integrate these properties at multiple length scales and match many aspects is highly desired. Here, we report a DNA-sequence based coarse-grained block copolymer model that considers different interactions between blocks of different CGI density, interactions of TAD formation, as well as interactions between chromatin and the nuclear envelope. This model captures the various single-chromosome properties and partially reproduces the formation of chromosome territories.

Predicting Genome Architecture: Challenges and Solutions

Genome architecture plays a pivotal role in gene regulation. The use of high-throughput methods for chromatin profiling and 3-D interaction mapping provide rich experimental data sets describing genome organization and dynamics. These data challenge development of new models and algorithms connecting genome architecture with epigenetic marks. In this review, we describe how chromatin architecture could be reconstructed from epigenetic data using biophysical or statistical approaches. We discuss the applicability and limitations of these methods for understanding the mechanisms of chromatin organization. We also highlight the emergence of new predictive approaches for scoring effects of structural variations in human cells.

Computational methods for the prediction of chromatin interaction and organization using sequence and epigenomic profiles

The exploration of three-dimensional chromatin interaction and organization provides insight into mechanisms underlying gene regulation, cell differentiation and disease development. Advances in chromosome conformation capture technologies, such as high-throughput chromosome conformation capture (Hi-C) and chromatin interaction analysis by paired-end tag (ChIA-PET), have enabled the exploration of chromatin interaction and organization. However, high-resolution Hi-C and ChIA-PET data are only available for a limited number of cell lines, and their acquisition is costly, time consuming, laborious and affected by theoretical limitations. Increasing evidence shows that DNA sequence and epigenomic features are informative predictors of regulatory interaction and chromatin architecture. Based on these features, numerous computational methods have been developed for the prediction of chromatin interaction and organization, whereas they are not extensively applied in biomedical study. A systematical study to summarize and evaluate such methods is still needed to facilitate their application. Here, we summarize 48 computational methods for the prediction of chromatin interaction and organization using sequence and epigenomic profiles, categorize them and compare their performance. Besides, we provide a comprehensive guideline for the selection of suitable methods to predict chromatin interaction and organization based on available data and biological question of interest.

Computational approaches for inferring 3D conformations of chromatin from chromosome conformation capture data

Chromosome conformation capture (3C) and its variants are powerful experimental techniques for probing intra- and inter-chromosomal interactions within cell nuclei at high resolution and in a high-throughput, quantitative manner. The contact maps derived from such experiments provide an avenue for inferring the 3D spatial organization of the genome. This review provides an overview of the various computational methods developed in the past decade for addressing the very important but challenging problem of deducing the detailed 3D structure or structure population of chromosomal domains, chromosomes, and even entire genomes from 3C contact maps.

The Interplay between Phase Separation and Gene-Enhancer Communication: A Theoretical Study

The phase separation occurring in a system of mutually interacting proteins that can bind on specific sites of a chromatin fiber is investigated here. This is achieved by means of extensive molecular dynamics simulations of a simple polymer model that includes regulatory proteins as interacting spherical particles. Our interest is particularly focused on the role played by phase separation in the formation of molecule aggregates that can join distant regulatory elements, such as gene promoters and enhancers, along the DNA. We find that the overall equilibrium state of the system resulting from the mutual interplay between binding molecules and chromatin can lead, under suitable conditions that depend on molecules concentration, molecule-molecule, and molecule-DNA interactions, to the formation of phase-separated molecular clusters, allowing robust contacts between regulatory sites. Vice versa, the presence of regulatory sites can promote the phase-separation process. Different dynamical regimes can generate the enhancer-promoter contact, either by cluster nucleation at binding sites or by bulk spontaneous formation of the mediating cluster to which binding sites are successively attracted. The possibility that such processes can explain experimental live-cell imaging data measuring distances between regulatory sites during time is also discussed.

Mechanistic modeling of chromatin folding to understand function

Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organization and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation of experimental results. Polymer simulations and mechanistic modeling have been applied to explain experimental observations and their links to different aspects of genome function. Here we provide a guide for biologists, explaining different simulation approaches and the contexts in which they have been used.

Integrating transposable elements in the 3D genome

Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) however, the spatial information of how genomes are folded is still only rarely integrated in experimental studies or accounted for in modelling. Whilst polymer physics is recognised as an important tool to understand the mechanisms of genome folding, in this commentary we discuss its potential applicability to aspects of TE biology. Based on recent works on the relationship between genome organisation and TE integration, we argue that existing polymer models may be extended to create a predictive framework for the study of TE integration patterns. We suggest that these models may offer orthogonal and generic insights into the integration profiles (or "topography") of TEs across organisms. In addition, we provide simple polymer physics arguments and preliminary molecular dynamics simulations of TEs inserting into heterogeneously flexible polymers. By considering this simple model, we show how polymer folding and local flexibility may generically affect TE integration patterns. The preliminary discussion reported in this commentary is aimed to lay the foundations for a large-scale analysis of TE integration dynamics and topography as a function of the three-dimensional host genome.

Bridging-induced microphase separation: photobleaching experiments, chromatin domains and the need for active reactions

We review the mechanism and consequences of the ‘bridging-induced attraction’, a generic biophysical principle that underpins some existing models for chromosome organization in 3D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains that conform well with the observation of A/B compartments in HiC experiments.

A comprehensive review of computational prediction of genome-wide features

There are significant correlations among different types of genetic, genomic and epigenomic features within the genome. These correlations make the in silico feature prediction possible through statistical or machine learning models. With the accumulation of a vast amount of high-throughput data, feature prediction has gained significant interest lately, and a plethora of papers have been published in the past few years. Here we provide a comprehensive review on these published works, categorized by the prediction targets, including protein binding site, enhancer, DNA methylation, chromatin structure and gene expression. We also provide discussions on some important points and possible future directions.

Polymer models for the mechanisms of chromatin 3D folding: review and perspective

In this perspective paper, classical physical models for mammalian interphase chromatin folding are reviewed.

Higher-order Chromosome Structures Investigated by Polymer Physics in Cellular Morphogenesis and Differentiation

Experimental advances in Molecular Biology demonstrated that chromatin architecture and gene regulation are deeply related. Hi-C data, for instance, returned a scenario where chromosomes form a complex pattern of interactions, including TADs, metaTADs, and compartments, correlated with genomic and epigenomic features. Here, we discuss the emerging hierarchical organization of chromatin and show how it remains partially conserved during mouse neuronal differentiation with changes highly related to modifications in gene expression. In this scenario, models of polymer physics, such as the Strings & Binders (SBS) model, can be a crucial instrument to understand the molecular mechanisms underlying the formation of such a higher order 3D structure. In particular, we focus on the case study of the murine Pitx1 genomic region. At this locus, two alternative spatial conformations take place in the hindlimb and forelimb tissues, corresponding to two different transcriptional states of Pitx1. We finally show how the structural variants can affect the locus 3D organization leading to ectopic gene expression and limb malformations.

7C: Computational Chromosome Conformation Capture by Correlation of ChIP-seq at CTCF motifs

BACKGROUND

Knowledge of the three-dimensional structure of the genome is necessary to understand how gene expression is regulated. Recent experimental techniques such as Hi-C or ChIA-PET measure long-range chromatin interactions genome-wide but are experimentally elaborate, have limited resolution and such data is only available for a limited number of cell types and tissues.

RESULTS

While ChIP-seq was not designed to detect chromatin interactions, the formaldehyde treatment in the ChIP-seq protocol cross-links proteins with each other and with DNA. Consequently, also regions that are not directly bound by the targeted TF but interact with the binding site via chromatin looping are co-immunoprecipitated and sequenced. This produces minor ChIP-seq signals at loop anchor regions close to the directly bound site. We use the position and shape of ChIP-seq signals around CTCF motif pairs to predict whether they interact or not. We implemented this approach in a prediction method, termed Computational Chromosome Conformation Capture by Correlation of ChIP-seq at CTCF motifs (7C). We applied 7C to all CTCF motif pairs within 1 Mb in the human genome and validated predicted interactions with high-resolution Hi-C and ChIA-PET. A single ChIP-seq experiment from known architectural proteins (CTCF, Rad21, Znf143) but also from other TFs (like TRIM22 or RUNX3) predicts loops accurately. Importantly, 7C predicts loops in cell types and for TF ChIP-seq datasets not used in training.

CONCLUSION

7C predicts chromatin loops which can help to associate TF binding sites to regulated genes. Furthermore, profiling of hundreds of ChIP-seq datasets results in novel candidate factors functionally involved in chromatin looping. Our method is available as an R/Bioconductor package: http://bioconductor.org/packages/sevenC .

Extrusion without a motor: a new take on the loop extrusion model of genome organization

Chromatin loop extrusion is a popular model for the formation of CTCF loops and topological domains. Recent HiC data have revealed a strong bias in favour of a particular arrangement of the CTCF binding motifs that stabilize loops, and extrusion is the only model to date which can explain this. However, the model requires a motor to generate the loops, and although cohesin is a strong candidate for the extruding factor, a suitable motor protein (or a motor activity in cohesin itself) has yet to be found. Here we explore a new hypothesis: that there is no motor, and thermal motion within the nucleus drives extrusion. Using theoretical modelling and computer simulations we ask whether such diffusive extrusion could feasibly generate loops. Our simulations uncover an interesting ratchet effect (where an osmotic pressure promotes loop growth), and suggest, by comparison to recent in vitro and in vivo measurements, that diffusive extrusion can in principle generate loops of the size observed in the data. Extra View on : C. A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi, P. R. Cook, and D. Marenduzzo “Non-equilibrium chromosome looping via molecular slip-links”, Physical Review Letters 119 138101 (2017)

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

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer three-dimensional folding of chromatin from Hi-C data. The three-dimensional chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from fluorescence in situ hybridization, chromatin interaction analysis by paired-end tag sequencing, and RNA-seq signals. We demonstrate the utility of the HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains from fluorescence in situ hybridization measurement, show the phase segregation between two types of topologically associated domains explicitly. We discuss the origin of cell-type-dependent gene-expression level by modeling the chromatin globules of α-globin and SOX2 gene loci for two different cell lines. We also use the HLM to discuss how the chromatin folding and gene-expression level of Pax6 loci, associated with mouse neural development, are modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells, based on single-cell Hi-C data collected over each cell-cycle phase, visualize changes in chromosome conformation along the cell-cycle. Given a contact frequency map between chromatic loci supplied from Hi-C, HLM is a computationally efficient and versatile modeling tool to generate chromosome structures that can complement interpreting other experimental data.

DamC reveals principles of chromatin folding in vivo without crosslinking and ligation

Current understanding of chromosome folding largely relies on chromosome conformation capture (3C)-based experiments, where chromosomal interactions are detected as ligation products after chromatin crosslinking. To measure chromosome structure in vivo, quantitatively and without crosslinking and ligation, we implemented a modified version of DamID named DamC, which combines DNA-methylation based detection of chromosomal interactions with next-generation sequencing and biophysical modelling of methylation kinetics. DamC performed in mouse embryonic stem cells provides the first in vivo validation of the existence of topologically associating domains (TADs), CTCF loops and confirms 3C-based measurements of the scaling of contact probabilities. Combining DamC with transposon-mediated genomic engineering shows that new loops can be formed between ectopic and endogenous CTCF sites, which redistributes physical interactions within TADs. DamC provides the first crosslinking- and ligation-free demonstration of the existence of key structural features of chromosomes and provides novel insights into how chromosome structure within TADs can be manipulated.

Chain organization of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

We investigate spatiotemporal dynamics of human interphase chromosomes by employing a heteropolymer model that incorporates the information of human chromosomes inferred from Hi-C data. Despite considerable heterogeneities in the chromosome structures generated from our model, chromatins are organized into crumpled globules with space-filling (SF) statistics characterized by a single universal scaling exponent (ν = 1/3), and this exponent alone can offer a quantitative account of experimentally observed, many different features of chromosome dynamics. The local chromosome structures, whose scale corresponds to that of topologically associated domains (∼ 0.1 − 1 Mb), display dynamics with a fast relaxation time (≲ 1 − 10 sec); in contrast, the long-range spatial reorganization of the entire chromatin (≳O(102) Mb) occurs on a much slower time scale (≳ hour), providing the dynamic basis of cell-to-cell variability and glass-like behavior of chromosomes. Biological activities, modeled using stronger isotropic white noises added to active loci, accelerate the relaxation dynamics of chromatin domains associated with the low frequency modes and induce phase segregation between the active and inactive loci. Surprisingly, however, they do not significantly change the dynamics at local scales from those obtained under passive conditions. Our study underscores the role of chain organization of chromosome in determining the spatiotemporal dynamics of chromatin loci.

Chromosomes are giant chain molecules made of hundreds of megabase-long DNA intercalated with proteins. Structure and dynamics of interphase chromatin in space and time hold the key to understanding the cell type-dependent gene regulation. In this study, we establish that the crumpled and space-filling (SF) organization of chromatin fiber in the chromosome territory, characterized by a single scaling exponent, is sufficient to explain the complex spatiotemporal hierarchy in chromatin dynamics as well as the subdiffusive motion of the chromatin loci. While seemingly a daunting problem at a first glance, our study shows that relatively simple principles, rooted in polymer physics, can be used to grasp the essence of dynamical properties of the interphase chromatin.

Exploring chromatin hierarchical organization via Markov State Modelling

We propose a new computational method for exploring chromatin structural organization based on Markov State Modelling of Hi-C data represented as an interaction network between genomic loci. A Markov process describes the random walk of a traveling probe in the corresponding energy landscape, mimicking the motion of a biomolecule involved in chromatin function. By studying the metastability of the associated Markov State Model upon annealing, the hierarchical structure of individual chromosomes is observed, and corresponding set of structural partitions is identified at each level of hierarchy. Then, the notion of effective interaction between partitions is derived, delineating the overall topology and architecture of chromosomes. Mapping epigenetic data on the graphs of intra-chromosomal effective interactions helps in understanding how chromosome organization facilitates its function. A sketch of whole-genome interactions obtained from the analysis of 539 partitions from all 23 chromosomes, complemented by distributions of gene expression regulators and epigenetic factors, sheds light on the structure-function relationships in chromatin, delineating chromosomal territories, as well as structural partitions analogous to topologically associating domains and active / passive epigenomic compartments. In addition to the overall genome architecture shown by effective interactions, the affinity between partitions of different chromosomes was analyzed as an indicator of the degree of association between partitions in functionally relevant genomic interactions. The overall static picture of whole-genome interactions obtained with the method presented in this work provides a foundation for chromatin structural reconstruction, for the modelling of chromatin dynamics, and for exploring the regulation of genome function. The algorithms used in this study are implemented in a freely available Python package ChromaWalker (https://bitbucket.org/ZhenWahTan/chromawalker).

A Polymer Model for the Quantitative Reconstruction of Chromosome Architecture from HiC and GAM Data

It is widely believed that the folding of the chromosome in the nucleus has a major effect on genetic expression. For example, coregulated genes in several species have been shown to colocalize in space despite being far away on the DNA sequence. In this manuscript, we present a new, to our knowledge, method to model the three-dimensional structure of the chromosome in live cells based on DNA-DNA interactions measured in high-throughput chromosome conformation capture experiments and genome architecture mapping. Our approach incorporates a polymer model and directly uses the contact probabilities measured in high-throughput chromosome conformation capture experiments and genome architecture mapping experiments rather than estimates of average distances between genomic loci. Specifically, we model the chromosome as a Gaussian polymer with harmonic interactions and extract the coupling coefficients best reproducing the experimental contact probabilities. In contrast to existing methods, we give an exact expression of the contact probabilities at thermodynamic equilibrium. The Gaussian effective model reconstructed with our method reproduces experimental contacts with high accuracy. We also show how Brownian dynamics simulations of our reconstructed Gaussian effective model can be used to study chromatin organization and possibly give some clue about its dynamics.

Polymer Simulations of Heteromorphic Chromatin Predict the 3D Folding of Complex Genomic Loci

Chromatin folded into 3D macromolecular structures is often analyzed by chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) techniques, but these frequently provide contradictory results. Chromatin can be modeled as a simple polymer composed of a connected chain of units. By embedding data for epigenetic marks (H3K27ac), chromatin accessibility (assay for transposase-accessible chromatin using sequencing [ATAC-seq]), and structural anchors (CCCTC-binding factor [CTCF]), we developed a highly predictive heteromorphic polymer (HiP-HoP) model, where the chromatin fiber varied along its length; combined with diffusing protein bridges and loop extrusion, this model predicted the 3D organization of genomic loci at a population and single-cell level. The model was validated at several gene loci, including the complex Pax6 gene, and was able to determine locus conformations across cell types with varying levels of transcriptional activity and explain different mechanisms of enhancer use. Minimal a priori knowledge of epigenetic marks is sufficient to recapitulate complex genomic loci in 3D and enable predictions of chromatin folding paths.

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HiP-HoP: highly predictive heteromorphic polymer model to analyze chromatin structure

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Polymer simulations use widely available epigenetic and protein binding data as input

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Validate HiP-HoP model at complex loci using 3D FISH and Capture-C

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Simulations uncover striking conformational variability in chromatin fiber folding

Dense neural networks for predicting chromatin conformation

Background

DNA inside eukaryotic cells wraps around histones to form the 11nm chromatin fiber that can further fold into higher-order DNA loops, which may depend on the binding of architectural factors. Predicting how the DNA will fold given a distribution of bound factors, here viewed as a type of sequence, is currently an unsolved problem and several heterogeneous polymer models have shown that many features of the measured structure can be reproduced from simulations. However a model that determines the optimal connection between sequence and structure and that can rapidly assess the effects of varying either one is still lacking.

Results

Here we train a dense neural network to solve for the local folding of chromatin, connecting structure, represented as a contact map, to a sequence of bound chromatin factors. The network includes a convolutional filter that compresses the large number of bound chromatin factors into a single 1D sequence representation that is optimized for predicting structure. We also train a network to solve the inverse problem, namely given only structural information in the form of a contact map, predict the likely sequence of chromatin states that generated it.

Conclusions

By carrying out sensitivity analysis on both networks, we are able to highlight the importance of chromatin contexts and neighborhoods for regulating long-range contacts, along with critical alterations that affect contact formation. Our analysis shows that the networks have learned physical insights that are informative and intuitive about this complex polymer problem.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2286-z) contains supplementary material, which is available to authorized users.

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.

HMGB2 Loss upon Senescence Entry Disrupts Genomic Organization and Induces CTCF Clustering across Cell Types

Processes like cellular senescence are characterized by complex events giving rise to heterogeneous cell populations. However, the early molecular events driving this cascade remain elusive. We hypothesized that senescence entry is triggered by an early disruption of the cells' three-dimensional (3D) genome organization. To test this, we combined Hi-C, single-cell and population transcriptomics, imaging, and in silico modeling of three distinct cells types entering senescence. Genes involved in DNA conformation maintenance are suppressed upon senescence entry across all cell types. We show that nuclear depletion of the abundant HMGB2 protein occurs early on the path to senescence and coincides with the dramatic spatial clustering of CTCF. Knocking down HMGB2 suffices for senescence-induced CTCF clustering and for loop reshuffling, while ectopically expressing HMGB2 rescues these effects. Our data suggest that HMGB2-mediated genomic reorganization constitutes a primer for the ensuing senescent program.

A maximum-entropy model for predicting chromatin contacts

The packaging of DNA inside a nucleus shows complex structure stabilized by a host of DNA-bound factors. Both the distribution of these factors and the contacts between different genomic locations of the DNA can now be measured on a genome-wide scale. This has advanced the development of models aimed at predicting the conformation of DNA given only the locations of bound factors-the chromatin folding problem. Here we present a maximum-entropy model that is able to predict a contact map representation of structure given a sequence of bound factors. Non-local effects due to the sequence neighborhood around contacting sites are found to be important for making accurate predictions. Lastly, we show that the model can be used to infer a sequence of bound factors given only a measurement of structure. This opens up the possibility for efficiently predicting sequence regions that may play a role in generating cell-type specific structural differences.