Hi-C-constrained physical models of human chromosomes recover functionally-related properties of genome organization

Chromatin as a Coevolutionary Graph: Modeling the Interplay of Replication with Chromatin Dynamics

Modeling DNA replication poses significant challenges due to the intricate interplay of biophysical processes and the need for precise parameter optimization. In this study, we explore the interactions among three key biophysical factors that influence chromatin folding: replication, loop extrusion, and compartmentalization. Replication forks, known to act as barriers to the motion of loop extrusion factors, also correlate with the phase separation of chromatin into A and B compartments. Our approach integrates three components: (1) a numerical model that takes into advantage single-cell replication timing data to simulate replication fork propagation; (2) a stochastic Monte Carlo simulation that captures the interplay between the biophysical factors, with loop extrusion factors binding, unbinding, and extruding dynamically, while CTCF barriers and replication forks act as static and moving barriers, and a Potts Hamiltonian governs the spreading of epigenetic states driving chromatin compartmentalization; and (3) a 3D OpenMM simulation that reconstructs the chromatin's 3D structure based on the states generated by the stochastic model. To our knowledge, this is the first framework to dynamically integrate and simulate these three biophysical factors, enabling insights into chromatin behavior during replication. Furthermore, we investigate how replication stress alters these dynamics and affects chromatin structure.

Organization and Dynamics of Chromosomes

How long thread-like eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which reproduce contact maps that measure the probabilities that two loci are in spatial contact, have predicted the 3D structures of interphase chromosomes. Data-driven approaches, using contact maps as input, predict that mitotic helical chromosomes are characterized by a switch in handedness, referred to as perversion. By using experimentally derived effective interactions between chromatin loci in simulations, structures of conventional and inverted nuclei have been accurately predicted. Polymer theory and simulations show that the dynamics of individual loci in chromatin exhibit subdiffusive behavior but the diffusion exponents are broadly distributed, which accords well with experiments. Although coarse-grained models are successful, many challenging problems remain, which require the creation of new experimental and computational tools to understand genome biology.

Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2 Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

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

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

Polymer physics models reveal structural folding features of single-molecule gene chromatin conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in-silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in-situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

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.

Reconstructing diploid 3D chromatin structures from single cell Hi-C data with a polymer-based approach

Detailed understanding of the 3D structure of chromatin is a key ingredient to investigate a variety of processes inside the cell. Since direct methods to experimentally ascertain these structures lack the desired spatial fidelity, computational inference methods based on single cell Hi-C data have gained significant interest. Here, we develop a progressive simulation protocol to iteratively improve the resolution of predicted interphase structures by maximum-likelihood association of ambiguous Hi-C contacts using lower-resolution predictions. Compared to state-of-the-art methods, our procedure is not limited to haploid cell data and allows us to reach a resolution of up to 5,000 base pairs per bead. High resolution chromatin models grant access to a multitude of structural phenomena. Exemplarily, we verify the formation of chromosome territories and holes near aggregated chromocenters as well as the inversion of the CpG content for rod photoreceptor cells.

Evaluating the role of the nuclear microenvironment in gene function by population-based modeling

The nuclear folding of chromosomes relative to nuclear bodies is an integral part of gene function. Here, we demonstrate that population-based modeling-from ensemble Hi-C data-provides a detailed description of the nuclear microenvironment of genes and its role in gene function. We define the microenvironment by the subnuclear positions of genomic regions with respect to nuclear bodies, local chromatin compaction, and preferences in chromatin compartmentalization. These structural descriptors are determined in single-cell models, thereby revealing the structural variability between cells. We demonstrate that the microenvironment of a genomic region is linked to its functional potential in gene transcription, replication, and chromatin compartmentalization. Some chromatin regions feature a strong preference for a single microenvironment, due to association with specific nuclear bodies in most cells. Other chromatin shows high structural variability, which is a strong indicator of functional heterogeneity. Moreover, we identify specialized nuclear microenvironments, which distinguish chromatin in different functional states and reveal a key role of nuclear speckles in chromosome organization. We demonstrate that our method produces highly predictive three-dimensional genome structures, which accurately reproduce data from a variety of orthogonal experiments, thus considerably expanding the range of Hi-C data analysis.

True-to-scale DNA-density maps correlate with major accessibility differences between active and inactive chromatin

Chromatin compaction differences may have a strong impact on accessibility of individual macromolecules and macromolecular assemblies to their DNA target sites. Estimates based on fluorescence microscopy with conventional resolution, however, suggest only modest compaction differences (∼2-10×) between the active nuclear compartment (ANC) and inactive nuclear compartment (INC). Here, we present maps of nuclear landscapes with true-to-scale DNA densities, ranging from <5 to >300 Mbp/μm3. Maps are generated from individual human and mouse cell nuclei with single-molecule localization microscopy at ∼20 nm lateral and ∼100 nm axial optical resolution and are supplemented by electron spectroscopic imaging. Microinjection of fluorescent nanobeads with sizes corresponding to macromolecular assemblies for transcription into nuclei of living cells demonstrates their localization and movements within the ANC and exclusion from the INC.

The magic of unraveling genome architecture and function

Over the last decades, technological breakthroughs in super-resolution microscopy have allowed us to reach molecular resolution and design experiments of unprecedented complexity. Investigating how chromatin is folded in 3D, from the nucleosome level up to the entire genome, is becoming possible by "magic" (imaging genomic), i.e., the combination of imaging and genomic approaches. This offers endless opportunities to delve into the relationship between genome structure and function. Here, we review recently achieved objectives and the conceptual and technical challenges the field of genome architecture is currently undertaking. We discuss what we have learned so far and where we are heading. We elucidate how the different super-resolution microscopy approaches and, more specifically, live-cell imaging have contributed to the understanding of genome folding. Moreover, we discuss how future technical developments could address remaining open questions.

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.

Satellite DNAs and human sex chromosome variation

Satellite DNAs are present on every chromosome in the cell and are typically enriched in repetitive, heterochromatic parts of the human genome. Sex chromosomes represent a unique genomic and epigenetic context. In this review, we first report what is known about satellite DNA biology on human X and Y chromosomes, including repeat content and organization, as well as satellite variation in typical euploid individuals. Then, we review sex chromosome aneuploidies that are among the most common types of aneuploidies in the general population, and are better tolerated than autosomal aneuploidies. This is demonstrated also by the fact that aging is associated with the loss of the X, and especially the Y chromosome. In addition, supernumerary sex chromosomes enable us to study general processes in a cell, such as analyzing heterochromatin dosage (i.e. additional Barr bodies and long heterochromatin arrays on Yq) and their downstream consequences. Finally, genomic and epigenetic organization and regulation of satellite DNA could influence chromosome stability and lead to aneuploidy. In this review, we argue that the complete annotation of satellite DNA on sex chromosomes in human, and especially in centromeric regions, will aid in explaining the prevalence and the consequences of sex chromosome aneuploidies.

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.

Biology and Model Predictions of the Dynamics and Heterogeneity of Chromatin-Nuclear Lamina Interactions

Associations of chromatin with the nuclear lamina, at the nuclear periphery, help shape the genome in 3 dimensions. The genomic landscape of lamina-associated domains (LADs) is well characterized, but much remains unknown on the physical and mechanistic properties of chromatin conformation at the nuclear lamina. Computational models of chromatin folding at, and interactions with, a surface representing the nuclear lamina are emerging in attempts to characterize these properties and predict chromatin behavior at the lamina in health and disease. Here, we highlight the heterogeneous nature of the nuclear lamina and LADs, outline the main 3-dimensional chromatin structural modeling methods, review applications of modeling chromatin-lamina interactions and discuss biological insights inferred from these models in normal and disease states. Lastly, we address perspectives on future developments in modeling chromatin interactions with the nuclear lamina.

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.

Physical mechanisms of chromatin spatial organization

In higher eukaryotes, chromosomes have a complex three-dimensional (3D) conformation in the cell nucleus serving vital functional purposes, yet their folding principles remain poorly understood at the single-molecule level. Here, we summarize recent approaches from polymer physics to comprehend the physical mechanisms underlying chromatin architecture. In particular, we focus on two models that have been supported by recent, growing experimental evidence, the Loop Extrusion model and the Strings&Binders phase separation model. We discuss their key ingredients, how they compare to experimental data and some insight they provide on chromatin architecture and gene regulation. Progress in that research field are opening the possibility to predict how genomic mutations alter the network of contacts between genes and their regulators and how that is linked to genetic diseases, such as congenital disorders and cancer.

Predicting genome organisation and function with mechanistic modelling

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future.

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.

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.

Understanding and Engineering Chromatin as a Dynamical System across Length and Timescales

Connecting the molecular structure and function of chromatin across length and timescales remains a grand challenge to understanding and engineering cellular behaviors. Across five orders of magnitude, dynamic processes constantly reshape chromatin structures, driving spaciotemporal patterns of gene expression and cell fate. Through the interplay of structure and function, the genome operates as a highly dynamic feedback control system. Recent experimental techniques have provided increasingly detailed data that revise and augment the relatively static, hierarchical view of genomic architecture with an understanding of how dynamic processes drive organization. Here, we review how novel technologies from sequencing, imaging, and synthetic biology refine our understanding of chromatin structure and function and enable chromatin engineering. Finally, we discuss opportunities to use these tools to enhance understanding of the dynamic interrelationship of chromatin structure and function.

Inferring chromosome radial organization from Hi-C data

BACKGROUND

The nonrandom radial organization of eukaryotic chromosome territories (CTs) inside the nucleus plays an important role in nuclear functional compartmentalization. Increasingly, chromosome conformation capture (Hi-C) based approaches are being used to characterize the genome structure of many cell types and conditions. Computational methods to extract 3D arrangements of CTs from this type of pairwise contact data will thus increase our ability to analyze CT organization in a wider variety of biological situations.

RESULTS

A number of full-scale polymer models have successfully reconstructed the 3D structure of chromosome territories from Hi-C. To supplement such methods, we explore alternative, direct, and less computationally intensive approaches to capture radial CT organization from Hi-C data. We show that we can infer relative chromosome ordering using PCA on a thresholded inter-chromosomal contact matrix. We simulate an ensemble of possible CT arrangements using a force-directed network layout algorithm and propose an approach to integrate additional chromosome properties into our predictions. Our CT radial organization predictions have a high correlation with microscopy imaging data for various cell nucleus geometries (lymphoblastoid, skin fibroblast, and breast epithelial cells), and we can capture previously documented changes in senescent and progeria cells.

CONCLUSIONS

Our analysis approaches provide rapid and modular approaches to screen for alterations in CT organization across widely available Hi-C data. We demonstrate which stages of the approach can extract meaningful information, and also describe limitations of pairwise contacts alone to predict absolute 3D positions.

Transcriptional activation during cell reprogramming correlates with the formation of 3D open chromatin hubs

Chromosome structure is a crucial regulatory factor for a wide range of nuclear processes. Chromosome conformation capture (3C)-based experiments combined with computational modelling are pivotal for unveiling 3D chromosome structure. Here, we introduce TADdyn, a tool that integrates time-course 3C data, restraint-based modelling, and molecular dynamics to simulate the structural rearrangements of genomic loci in a completely data-driven way. We apply TADdyn on in situ Hi-C time-course experiments studying the reprogramming of murine B cells to pluripotent cells, and characterize the structural rearrangements that take place upon changes in the transcriptional state of 21 genomic loci of diverse expression dynamics. By measuring various structural and dynamical properties, we find that during gene activation, the transcription starting site contacts with open and active regions in 3D chromatin domains. We propose that these 3D hubs of open and active chromatin may constitute a general feature to trigger and maintain gene transcription.

Impact of Chromosome Fusions on 3D Genome Organization and Gene Expression in Budding Yeast

The three-dimensional (3D) organization of chromosomes can influence transcription. However, the frequency and magnitude of these effects remain debated. To determine how changes in chromosome positioning affect transcription across thousands of genes with minimal perturbation, we characterized nuclear organization and global gene expression in budding yeast containing chromosome fusions. We used computational modeling and single-cell imaging to determine chromosome positions, and integrated these data with genome-wide transcriptional profiles from RNA sequencing. We find that chromosome fusions dramatically alter 3D nuclear organization without leading to strong genome-wide changes in transcription. However, we observe a mild but significant and reproducible increase in the expression of genes displaced away from the periphery. The increase in transcription is inversely proportional to the propensity of a given locus to be at the nuclear periphery; for example, a 10% decrease in the propensity of a gene to reside at the nuclear envelope is accompanied by a 10% increase in gene expression. Modeling suggests that this is due to both deletion of telomeres and to displacement of genes relative to the nuclear periphery. These data suggest that basal transcriptional activity is sensitive to radial changes in gene position, and provide insight into the functional relevance of budding yeast chromosome-level 3D organization in gene expression.

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.

Merging 1D and 3D genomic information: Challenges in modelling and validation

Genome organization in eukaryotes during interphase stems from the delicate balance between non-random correlations present in the DNA polynucleotide linear sequence and the physico/chemical reactions which shape continuously the form and structure of DNA and chromatin inside the nucleus of the cell. It is now clear that these mechanisms have a key role in important processes like gene regulation, yet the detailed ways they act simultaneously and, eventually, come to influence each other even across very different length-scales remain largely unexplored. In this paper, we recapitulate some of the main results concerning gene regulatory and physical mechanisms, in relation to the information encoded in the 1D sequence and the 3D folding structure of DNA. In particular, we stress how reciprocal crossfeeding between 1D and 3D models may provide original insight into how these complex processes work and influence each other. This article is part of a Special Issue entitled: Transcriptional Profiles and Regulatory Gene Networks edited by Dr. Dr. Federico Manuel Giorgi and Dr. Shaun Mahony.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Defining and detecting links in chromosomes

Sophisticated methods for mapping chromatin contacts enable to generate data of the genome structure that provide deep insights into the formation of chromatin interactions within cell nuclei. Due to the recent progress in this field, three-dimensional genomic structures of individual haploid mouse embryonic stem cells have been determined. Here, we analyze these data (8 cells) and determine comprehensive landscape of entanglements between interphase chromosomes. We find a significant number of stable links formed by chromosome pairs. Some links are even conserved between cells. Moreover, examples of stable multiple links, with at least three chromosomes engaged, are also identified. Types of links and their location along chromosomes are determined based on computations of HOMFLY-PT polynomials and Gauss Linking Numbers. Furthermore, stability of links is studied between different models, cells, and based on relaxation simulations of the genomic structure in a simplified structure-based representation. Identified links suggest that small fraction of chromosomes are entangled not only locally. How topoisomerases engineer such configurations remains an open question. Furthermore, presented methods can be used as a quantitative assessment - descriptor - to distinguish the quality of modeled data.

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.

Models of polymer physics for the architecture of the cell nucleus

The depth and complexity of data now available on chromosome 3D architecture, derived by new technologies such as Hi-C, have triggered the development of models based on polymer physics to explain the observed patterns and the underlying molecular folding mechanisms. Here, we give an overview of some of the ideas and models from physics introduced to date, along with their progresses and limitations in the description of experimental data. In particular, we focus on the Strings&Binders and the Loop Extrusion model of chromatin architecture. This article is categorized under: Analytical and Computational Methods > Computational Methods.

Human pancreatic islet three-dimensional chromatin architecture provides insights into the genetics of type 2 diabetes

Genetic studies promise to provide insight into the molecular mechanisms underlying type 2 diabetes (T2D). Variants associated with T2D are often located in tissue-specific enhancer clusters or super-enhancers. So far, such domains have been defined through clustering of enhancers in linear genome maps rather than in three-dimensional (3D) space. Furthermore, their target genes are often unknown. We have created promoter capture Hi-C maps in human pancreatic islets. This linked diabetes-associated enhancers to their target genes, often located hundreds of kilobases away. It also revealed >1,300 groups of islet enhancers, super-enhancers and active promoters that form 3D hubs, some of which show coordinated glucose-dependent activity. We demonstrate that genetic variation in hubs impacts insulin secretion heritability, and show that hub annotations can be used for polygenic scores that predict T2D risk driven by islet regulatory variants. Human islet 3D chromatin architecture, therefore, provides a framework for interpretation of T2D genome-wide association study (GWAS) signals.

Estimation of the Spatial Chromatin Structure Based on a Multiresolution Bead-Chain Model

We present a method to infer 3D chromatin configurations from Chromosome Conformation Capture data. Quite a few methods have been proposed to estimate the structure of the nuclear dna in homogeneous populations of cells from this kind of data. Many of them transform contact frequencies into euclidean distances between pairs of chromatin fragments, and then reconstruct the structure by solving a distance-to-geometry problem. To avoid inconsistencies, our method is based on a score function that does not require any frequency-to-distance translation. We propose a multiscale chromatin model where the chromatin fiber is suitably partitioned at each scale. The partial structures are estimated independently, and connected to rebuild the whole fiber. Our score function consists of a data-fit part and a penalty part, balanced automatically at each scale and each subchain. The penalty part enforces soft geometric constraints. As many different structures can fit the data, our sampling strategy produces a set of solutions with similar scores. The procedure contains a few parameters, independent of both the scale and the genomic segment treated. The partition of the fiber, along with intrinsically parallel parts, make this method computationally efficient. Results from human genome data support the biological plausibility of our solutions.

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.

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

Capsid-CPSF6 Interaction Licenses Nuclear HIV-1 Trafficking to Sites of Viral DNA Integration

HIV-1 integration into the host genome favors actively transcribed genes. Prior work indicated that the nuclear periphery provides the architectural basis for integration site selection, with viral capsid-binding host cofactor CPSF6 and viral integrase-binding cofactor LEDGF/p75 contributing to selection of individual sites. Here, by investigating the early phase of infection, we determine that HIV-1 traffics throughout the nucleus for integration. CPSF6-capsid interactions allow the virus to bypass peripheral heterochromatin and penetrate the nuclear structure for integration. Loss of interaction with CPSF6 dramatically alters virus localization toward the nuclear periphery and integration into transcriptionally repressed lamina-associated heterochromatin, while loss of LEDGF/p75 does not significantly affect intranuclear HIV-1 localization. Thus, CPSF6 serves as a master regulator of HIV-1 intranuclear localization by trafficking viral preintegration complexes away from heterochromatin at the periphery toward gene-dense chromosomal regions within the nuclear interior.

Epigenomic annotation-based interpretation of genomic data: from enrichment analysis to machine learning

Motivation

One of the goals of functional genomics is to understand the regulatory implications of experimentally obtained genomic regions of interest (ROIs). Most sequencing technologies now generate ROIs distributed across the whole genome. The interpretation of these genome-wide ROIs represents a challenge as the majority of them lie outside of functionally well-defined protein coding regions. Recent efforts by the members of the International Human Epigenome Consortium have generated volumes of functional/regulatory data (reference epigenomic datasets), effectively annotating the genome with epigenomic properties. Consequently, a wide variety of computational tools has been developed utilizing these epigenomic datasets for the interpretation of genomic data.

Results

The purpose of this review is to provide a structured overview of practical solutions for the interpretation of ROIs with the help of epigenomic data. Starting with epigenomic enrichment analysis, we discuss leading tools and machine learning methods utilizing epigenomic and 3D genome structure data. The hierarchy of tools and methods reviewed here presents a practical guide for the interpretation of genome-wide ROIs within an epigenomic context.

Contact

mikhail.dozmorov@vcuhealth.org.

Supplementary information

Supplementary data are available at Bioinformatics online.

ChromStruct 4: A Python Code to Estimate the Chromatin Structure from Hi-C Data

A method and a stand-alone Python(TM) code to estimate the 3D chromatin structure from chromosome conformation capture data are presented. The method is based on a multiresolution, modified-bead-chain chromatin model, evolved through quaternion operators in a Monte Carlo sampling. The solution space to be sampled is generated by a score function with a data-fit part and a constraint part where the available prior knowledge is implicitly coded. The final solution is a set of 3D configurations that are compatible with both the data and the prior knowledge. The iterative code, provided here as additional material, is equipped with a graphical user interface and stores its results in standard-format files for 3D visualization. We describe the mathematical-computational aspects of the method and explain the details of the code. Some experimental results are reported, with a demonstration of their fit to the data.

Reprogramming, oscillations and transdifferentiation in epigenetic landscapes

Waddington’s epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

Chromatin Architectural Changes during Cellular Senescence and Aging

Chromatin 3D structure is highly dynamic and associated with many biological processes, such as cell cycle progression, cellular differentiation, cell fate reprogramming, cancer development, cellular senescence, and aging. Recently, by using chromosome conformation capture technologies, tremendous findings have been reported about the dynamics of genome architecture, their associated proteins, and the underlying mechanisms involved in regulating chromatin spatial organization and gene expression. Cellular senescence and aging, which involve multiple cellular and molecular functional declines, also undergo significant chromatin structural changes, including alternations of heterochromatin and disruption of higher-order chromatin structure. In this review, we summarize recent findings related to genome architecture, factors regulating chromatin spatial organization, and how they change during cellular senescence and aging.

A Polymer Physics Investigation of the Architecture of the Murine Orthologue of the 7q11.23 Human Locus

In the last decade, the developments of novel technologies, such as Hi-C or GAM methods, allowed to discover that chromosomes in the nucleus of mammalian cells have a complex spatial organization, encompassing the functional contacts between genes and regulators. In this work, we review recent progresses in chromosome modeling based on polymer physics to understand chromatin structure and folding mechanisms. As an example, we derive in mouse embryonic stem cells the full 3D structure of the Bmp7 locus, a genomic region that plays a key role in osteoblastic differentiation. Next, as an application to Neuroscience, we present the first 3D model for the mouse orthologoue of the Williams-Beuren syndrome 7q11.23 human locus. Deletions and duplications of the 7q11.23 region generate neurodevelopmental disorders with multi-system involvement and variable expressivity, and with autism. Understanding the impact of such mutations on the rewiring of the interactions of genes and regulators could be a new key to make sense of their related diseases, with potential applications in biomedicine.

GRID-seq reveals the global RNA-chromatin interactome

Higher eukaryotic genomes are bound by a large number of coding and non-coding RNAs, but approaches to comprehensively map the identity and binding sites of these RNAs are lacking. Here we report a method to capture in situ global RNA interactions with DNA by deep sequencing (GRID-seq), which enables the comprehensive identification of the entire repertoire of chromatin-interacting RNAs and their respective binding sites. In human, mouse, and Drosophila cells, we detected a large set of tissue-specific coding and non-coding RNAs that are bound to active promoters and enhancers, especially super-enhancers. Assuming that most mRNA-chromatin interactions indicate the physical proximity of a promoter and an enhancer, we constructed a three-dimensional global connectivity map of promoters and enhancers, revealing transcription-activity-linked genomic interactions in the nucleus.

Challenges for visualizing three-dimensional data in genomic browsers

Genomic interactions reveal the spatial organization of genomes and genomic domains, which is known to play key roles in cell function. Physical proximity can be represented as two-dimensional heat maps or matrices. From these, three-dimensional (3D) conformations of chromatin can be computed revealing coherent structures that highlight the importance of nonsequential relationships across genomic features. Mainstream genomic browsers have been classically developed to display compact, stacked tracks based on a linear, sequential, per-chromosome coordinate system. Genome-wide comparative analysis demands new approaches to data access and new layouts for analysis. The legibility can be compromised when displaying track-aligned second dimension matrices, which require greater screen space. Moreover, 3D representations of genomes defy vertical alignment in track-based genome browsers. Furthermore, investigation at previously unattainable levels of detail is revealing multiscale, multistate, time-dependent complexity. This article outlines how these challenges are currently handled in mainstream browsers as well as how novel techniques in visualization are being explored to address them. A set of requirements for coherent visualization of novel spatial genomic data is defined and the resulting potential for whole genome visualization is described.