Genome structure determination via 3C-based data integration by the Integrative Modeling Platform

Identifying TAD-like domains on single-cell Hi-C data by graph embedding and changepoint detection

MOTIVATION

Topologically associating domains (TADs) are fundamental building blocks of 3D genome. TAD-like domains in single cells are regarded as the underlying genesis of TADs discovered in bulk cells. Understanding the organization of TAD-like domains helps to get deeper insights into their regulatory functions. Unfortunately, it remains a challenge to identify TAD-like domains on single-cell Hi-C data due to its ultra-sparsity.

RESULTS

We propose scKTLD, an in silico tool for the identification of TAD-like domains on single-cell Hi-C data. It takes Hi-C contact matrix as the adjacency matrix for a graph, embeds the graph structures into a low-dimensional space with the help of sparse matrix factorization followed by spectral propagation, and the TAD-like domains can be identified using a kernel-based changepoint detection in the embedding space. The results tell that our scKTLD is superior to the other methods on the sparse contact matrices, including downsampled bulk Hi-C data as well as simulated and experimental single-cell Hi-C data. Besides, we demonstrated the conservation of TAD-like domain boundaries at single-cell level apart from heterogeneity within and across cell types, and found that the boundaries with higher frequency across single cells are more enriched for architectural proteins and chromatin marks, and they preferentially occur at TAD boundaries in bulk cells, especially at those with higher hierarchical levels.

AVAILABILITY AND IMPLEMENTATION

scKTLD is freely available at https://github.com/lhqxinghun/scKTLD.

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

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

Interplay between epigenome and 3D chromatin structure

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

The Physics of DNA Folding: Polymer Models and Phase-Separation

Within cell nuclei, several biophysical processes occur in order to allow the correct activities of the genome such as transcription and gene regulation. To quantitatively investigate such processes, polymer physics models have been developed to unveil the molecular mechanisms underlying genome functions. Among these, phase-separation plays a key role since it controls gene activity and shapes chromatin spatial structure. In this paper, we review some recent experimental and theoretical progress in the field and show that polymer physics in synergy with numerical simulations can be helpful for several purposes, including the study of molecular condensates, gene-enhancer dynamics, and the three-dimensional reconstruction of real genomic regions.

Coordinated changes in gene expression, H1 variant distribution and genome 3D conformation in response to H1 depletion

Up to seven members of the histone H1 family may contribute to chromatin compaction and its regulation in human somatic cells. In breast cancer cells, knock-down of multiple H1 variants deregulates many genes, promotes the appearance of genome-wide accessibility sites and triggers an interferon response via activation of heterochromatic repeats. However, how these changes in the expression profile relate to the re-distribution of H1 variants as well as to genome conformational changes have not been yet studied. Here, we combined ChIP-seq of five endogenous H1 variants with Chromosome Conformation Capture analysis in wild-type and H1.2/H1.4 knock-down T47D cells. The results indicate that H1 variants coexist in the genome in two large groups depending on the local GC content and that their distribution is robust with respect to H1 depletion. Despite the small changes in H1 variants distribution, knock-down of H1 translated into more isolated but de-compacted chromatin structures at the scale of topologically associating domains (TADs). Such changes in TAD structure correlated with a coordinated gene expression response of their resident genes. This is the first report describing simultaneous profiling of five endogenous H1 variants and giving functional evidence of genome topology alterations upon H1 depletion in human cancer cells.

Modeling the 3D genome of plants

Chromosomes are the carriers of inheritable traits and define cell function and development. This is not only based on the linear DNA sequence of chromosomes but also on the additional molecular information they are associated with, including the transcription machinery, histone modifications, and their three-dimensional folding. The synergistic application of experimental approaches and computer simulations has helped to unveil how these organizational layers of the genome interplay in various organisms. However, such multidisciplinary approaches are still rarely explored in the plant kingdom. Here, we provide an overview of our current knowledge on plant 3D genome organization and review recent efforts to integrate cutting-edge experiments from microscopy and next-generation sequencing approaches with theoretical models. Building on these recent approaches, we propose possible avenues to extend the application of theoretical modeling in the characterization of the 3D genome organization in plants.

Minimalistic 3D chromatin models: Sparse interactions in single cells drive the chromatin fold and form many-body units

Computational three-dimensional chromatin modeling has helped uncover principles of genome organization. Here, we discuss methods for modeling three-dimensional chromatin structures, with focus on a minimalistic polymer model which inverts population Hi-C into single-cell conformations. Utilizing only basic physical properties, this model reveals that a few specific Hi-C interactions can fold chromatin into conformations consistent with single-cell imaging, Dip-C, and FISH measurements. Aggregated single-cell chromatin conformations also reproduce Hi-C frequencies. This approach allows quantification of structural heterogeneity and discovery of many-body interaction units and has revealed additional insights, including (1) topologically associating domains as a byproduct of folding driven by specific interactions, (2) cell subpopulations with different structural scaffolds are developmental stage dependent, and (3) the functional landscape of many-body units within enhancer-rich regions. We also discuss these findings in relation to the genome structure-function relationship.

DeTOKI identifies and characterizes the dynamics of chromatin TAD-like domains in a single cell

Topologically associating domains (TAD) are a key structure of the 3D mammalian genomes. However, the prevalence and dynamics of TAD-like domains in single cells remain elusive. Here we develop a new algorithm, named deTOKI, to decode TAD-like domains with single-cell Hi-C data. By non-negative matrix factorization, deTOKI seeks regions that insulate the genome into blocks with minimal chance of clustering. deTOKI outperforms competing tools and reliably identifies TAD-like domains in single cells. Finally, we find that TAD-like domains are not only prevalent, but also subject to tight regulation in single cells.

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.

The 3D Genome Structure of Single Cells

The spatial organization of the genome in the cell nucleus is pivotal to cell function. However, how the 3D genome organization and its dynamics influence cellular phenotypes remains poorly understood. The very recent development of single-cell technologies for probing the 3D genome, especially single-cell Hi-C (scHi-C), has ushered in a new era of unveiling cell-to-cell variability of 3D genome features at an unprecedented resolution. Here, we review recent developments in computational approaches to the analysis of scHi-C, including data processing, dimensionality reduction, imputation for enhancing data quality, and the revealing of 3D genome features at single-cell resolution. While much progress has been made in computational method development to analyze single-cell 3D genomes, substantial future work is needed to improve data interpretation and multimodal data integration, which are critical to reveal fundamental connections between genome structure and function among heterogeneous cell populations in various biological contexts.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Computational methods for predicting 3D genomic organization from high-resolution chromosome conformation capture data

The advent of high-resolution chromosome conformation capture assays (such as 5C, Hi-C and Pore-C) has allowed for unprecedented sequence-level investigations into the structure-function relationship of the genome. In order to comprehensively understand this relationship, computational tools are required that utilize data generated from these assays to predict 3D genome organization (the 3D genome reconstruction problem). Many computational tools have been developed that answer this need, but a comprehensive comparison of their underlying algorithmic approaches has not been conducted. This manuscript provides a comprehensive review of the existing computational tools (from November 2006 to September 2019, inclusive) that can be used to predict 3D genome organizations from high-resolution chromosome conformation capture data. Overall, existing tools were found to use a relatively small set of algorithms from one or more of the following categories: dimensionality reduction, graph/network theory, maximum likelihood estimation (MLE) and statistical modeling. Solutions in each category are far from maturity, and the breadth and depth of various algorithmic categories have not been fully explored. While the tools for predicting 3D structure for a genomic region or single chromosome are diverse, there is a general lack of algorithmic diversity among computational tools for predicting the complete 3D genome organization from high-resolution chromosome conformation capture data.

Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis-Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

Dynamics of genome architecture and chromatin function during human B cell differentiation and neoplastic transformation

To investigate the three-dimensional (3D) genome architecture across normal B cell differentiation and in neoplastic cells from different subtypes of chronic lymphocytic leukemia and mantle cell lymphoma patients, here we integrate in situ Hi-C and nine additional omics layers. Beyond conventional active (A) and inactive (B) compartments, we uncover a highly-dynamic intermediate compartment enriched in poised and polycomb-repressed chromatin. During B cell development, 28% of the compartments change, mostly involving a widespread chromatin activation from naive to germinal center B cells and a reversal to the naive state upon further maturation into memory B cells. B cell neoplasms are characterized by both entity and subtype-specific alterations in 3D genome organization, including large chromatin blocks spanning key disease-specific genes. This study indicates that 3D genome interactions are extensively modulated during normal B cell differentiation and that the genome of B cell neoplasias acquires a tumor-specific 3D genome architecture.

A new precision medicine initiative at the dawn of exascale computing

Which signaling pathway and protein to select to mitigate the patient's expected drug resistance? The number of possibilities facing the physician is massive, and the drug combination should fit the patient status. Here, we briefly review current approaches and data and map an innovative patient-specific strategy to forecast drug resistance targets that centers on parallel (or redundant) proliferation pathways in specialized cells. It considers the availability of each protein in each pathway in the specific cell, its activating mutations, and the chromatin accessibility of its encoding gene. The construction of the resulting Proliferation Pathway Network Atlas will harness the emerging exascale computing and advanced artificial intelligence (AI) methods for therapeutic development. Merging the resulting set of targets, pathways, and proteins, with current strategies will augment the choice for the attending physicians to thwart resistance.

Data-Driven Polymer Model for Mechanistic Exploration of Diploid Genome Organization

Chromosomes are positioned nonrandomly inside the nucleus to coordinate with their transcriptional activity. The molecular mechanisms that dictate the global genome organization and the nuclear localization of individual chromosomes are not fully understood. We introduce a polymer model to study the organization of the diploid human genome. It is data-driven because all parameters can be derived from Hi-C data; it is also a mechanistic model because the energy function is explicitly written out based on a few biologically motivated hypotheses. These two features distinguish the model from existing approaches and make it useful both for reconstructing genome structures and for exploring the principles of genome organization. We carried out extensive validations to show that simulated genome structures reproduce a wide variety of experimental measurements, including chromosome radial positions and spatial distances between homologous pairs. Detailed mechanistic investigations support the importance of both specific interchromosomal interactions and centromere clustering for chromosome positioning. We anticipate the polymer model, when combined with Hi-C experiments, to be a powerful tool for investigating large-scale rearrangements in genome structure upon cell differentiation and tumor progression.

Analysis, Modeling, and Visualization of Chromosome Conformation Capture Experiments

Chromatin Conformation Capture techniques have unveiled several layers of chromosome organization such as the segregation in compartments, the folding in topologically associating domains (TADs), and site-specific looping interactions. The discovery of this genome hierarchical organization emerged from the computational analysis of chromatin capture data. With the increasing availability of such data, automatic pipelines for the robust comparison, grouping, and classification of multiple experiments are needed. Here we present a pipeline based on the TADbit framework that emphasizes reproducibility, automation, quality check, and statistical robustness. This comprehensive modular pipeline covers all the steps from the sequencing products to the visualization of reconstructed 3D models of the chromatin.

Chromatin 3D structure reconstruction with consideration of adjacency relationship among genomic loci

BACKGROUND

Chromatin 3D conformation plays important roles in regulating gene or protein functions. High-throughout chromosome conformation capture (3C)-based technologies, such as Hi-C, have been exploited to acquire the contact frequencies among genomic loci at genome-scale. Various computational tools have been proposed to recover the underlying chromatin 3D structures from in situ Hi-C contact map data. As connected residuals in a polymer, neighboring genomic loci have intrinsic mutual dependencies in building a 3D conformation. However, current methods seldom take this feature into account.

RESULTS

We present a method called ShNeigh, which combines the classical MDS technique with local dependence of neighboring loci modeled by a Gaussian formula, to infer the best 3D structure from noisy and incomplete contact frequency matrices. We validated ShNeigh by comparing it to two typical distance-based algorithms, ShRec3D and ChromSDE. The comparison results on simulated Hi-C dataset showed that, while keeping the high-speed nature of classical MDS, ShNeigh can recover the true structure better than ShRec3D and ChromSDE. Meanwhile, ShNeigh is more robust to data noise. On the publicly available human GM06990 Hi-C data, we demonstrated that the structures reconstructed by ShNeigh are more reproducible between different restriction enzymes than by ShRec3D and ChromSDE, especially at high resolutions manifested by sparse contact maps, which means ShNeigh is more robust to signal coverage.

CONCLUSIONS

Our method can recover stable structures in high noise and sparse signal settings. It can also reconstruct similar structures from Hi-C data obtained using different restriction enzymes. Therefore, our method provides a new direction for enhancing the reconstruction quality of chromatin 3D structures.

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.

4D Genome Rewiring during Oncogene-Induced and Replicative Senescence

To understand the role of the extensive senescence-associated 3D genome reorganization, we generated genome-wide chromatin interaction maps, epigenome, replication-timing, whole-genome bisulfite sequencing, and gene expression profiles from cells entering replicative senescence (RS) or upon oncogene-induced senescence (OIS). We identify senescence-associated heterochromatin domains (SAHDs). Differential intra- versus inter-SAHD interactions lead to the formation of senescence-associated heterochromatin foci (SAHFs) in OIS but not in RS. This OIS-specific configuration brings active genes located in genomic regions adjacent to SAHDs in close spatial proximity and favors their expression. We also identify DNMT1 as a factor that induces SAHFs by promoting HMGA2 expression. Upon DNMT1 depletion, OIS cells transition to a 3D genome conformation akin to that of cells in replicative senescence. These data show how multi-omics and imaging can identify critical features of RS and OIS and discover determinants of acute senescence and SAHF formation.

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Deep multi-omics characterization of replicative and oncogene-induced senescence

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Senescence-associated heterochromatin domains (SAHDs) form SAHFs via 3D changes

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DNMT1 is required for SAHF formation via regulation of HMGA2 expression

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SAHF formation leads to expression of SAHF-adjacent genes via 3D chromatin contacts

Laminopathy-causing lamin A mutations reconfigure lamina-associated domains and local spatial chromatin conformation

The nuclear lamina contributes to the regulation of gene expression and to chromatin organization. Mutations in A-type nuclear lamins cause laminopathies, some of which are associated with a loss of heterochromatin at the nuclear periphery. Until recently however, little if any information has been provided on where and how lamin A interacts with the genome and on how disease-causing lamin A mutations may rearrange genome conformation. Here, we review aspects of nuclear lamin association with the genome. We highlight recent evidence of reorganization of lamin A-chromatin interactions in cellular models of laminopathies, and implications on the 3-dimensional rearrangement of chromatin in these models, including patient cells. We discuss how a hot-spot lipodystrophic lamin A mutation alters chromatin conformation and epigenetic patterns at an anti-adipogenic locus, and conclude with remarks on links between lamin A, Polycomb and the pathophysiology of laminopathies. The recent findings presented here collectively argue towards a deregulation of large-scale and local spatial genome organization by a subset of lamin A mutations causing laminopathies.

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.

Finding Friends in the Crowd: Three-Dimensional Cliques of Topological Genomic Domains

The mammalian genome is intricately folded in a three-dimensional topology believed to be important for the orchestration of gene expression regulating development, differentiation and tissue homeostasis. Important features of spatial genome conformation in the nucleus are promoter-enhancer contacts regulating gene expression within topologically-associated domains (TADs), short- and long-range interactions between TADs and associations of chromatin with nucleoli and nuclear speckles. In addition, anchoring of chromosomes to the nuclear lamina via lamina-associated domains (LADs) at the nuclear periphery is a key regulator of the radial distribution of chromatin. To what extent TADs and LADs act in concert as genomic organizers to shape the three-dimensional topology of chromatin has long remained unknown. A new study addressing this key question provides evidence of (i) preferred long-range associations between TADs forming TAD “cliques” which organize large heterochromatin domains, and (ii) stabilization of TAD cliques by LADs at the nuclear periphery after induction of terminal differentiation. Here, we review these findings, address the issue of whether TAD cliques exist in single cells and discuss the extent of cell-to-cell heterogeneity in higher-order chromatin conformation. The recent observations provide a first appreciation of changes in 4-dimensional higher-order genome topologies during differentiation.

Bayesian Estimation of Three-Dimensional Chromosomal Structure from Single-Cell Hi-C Data

The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is important and challenging. While bulk Hi-C data sets contain contact information derived from millions of cells and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single-cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named Structural Inference via Multiscale Bayesian Approach, to infer 3D structures of chromosomes from single-cell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C data set as a function of prior strength and demonstrate clustering of solutions using data from the same cell.

An Overview of Methods for Reconstructing 3-D Chromosome and Genome Structures from Hi-C Data

Over the past decade, methods for predicting three-dimensional (3-D) chromosome and genome structures have proliferated. This has been primarily due to the development of high-throughput, next-generation chromosome conformation capture (3C) technologies, which have provided next-generation sequencing data about chromosome conformations in order to map the 3-D genome structure. The introduction of the Hi-C technique-a variant of the 3C method-has allowed researchers to extract the interaction frequency (IF) for all loci of a genome at high-throughput and at a genome-wide scale. In this review we describe, categorize, and compare the various methods developed to map chromosome and genome structures from 3C data-particularly Hi-C data. We summarize the improvements introduced by these methods, describe the approach used for method evaluation, and discuss how these advancements shape the future of genome structure construction.

Hierarchical Reconstruction of High-Resolution 3D Models of Large Chromosomes

Eukaryotic chromosomes are often composed of components organized into multiple scales, such as nucleosomes, chromatin fibers, topologically associated domains (TAD), chromosome compartments, and chromosome territories. Therefore, reconstructing detailed 3D models of chromosomes in high resolution is useful for advancing genome research. However, the task of constructing quality high-resolution 3D models is still challenging with existing methods. Hence, we designed a hierarchical algorithm, called Hierarchical3DGenome, to reconstruct 3D chromosome models at high resolution (<=5 Kilobase (KB)). The algorithm first reconstructs high-resolution 3D models at TAD level. The TAD models are then assembled to form complete high-resolution chromosomal models. The assembly of TAD models is guided by a complete low-resolution chromosome model. The algorithm is successfully used to reconstruct 3D chromosome models at 5 KB resolution for the human B-cell (GM12878). These high-resolution models satisfy Hi-C chromosomal contacts well and are consistent with models built at lower (i.e. 1 MB) resolution, and with the data of fluorescent in situ hybridization experiments. The Java source code of Hierarchical3DGenome and its user manual are available here https://github.com/BDM-Lab/Hierarchical3DGenome .

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.

Walking along chromosomes with super-resolution imaging, contact maps, and integrative modeling

Chromosome organization is crucial for genome function. Here, we present a method for visualizing chromosomal DNA at super-resolution and then integrating Hi-C data to produce three-dimensional models of chromosome organization. Using the super-resolution microscopy methods of OligoSTORM and OligoDNA-PAINT, we trace 8 megabases of human chromosome 19, visualizing structures ranging in size from a few kilobases to over a megabase. Focusing on chromosomal regions that contribute to compartments, we discover distinct structures that, in spite of considerable variability, can predict whether such regions correspond to active (A-type) or inactive (B-type) compartments. Imaging through the depths of entire nuclei, we capture pairs of homologous regions in diploid cells, obtaining evidence that maternal and paternal homologous regions can be differentially organized. Finally, using restraint-based modeling to integrate imaging and Hi-C data, we implement a method-integrative modeling of genomic regions (IMGR)-to increase the genomic resolution of our traces to 10 kb.

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.

Modeling three-dimensional genomic organization in evolution and pathogenesis

The regulation of gene expression is mediated via the complex three-dimensional (3D) conformation of the genetic material and its interactions with various intracellular factors. Various experimental and computational approaches have been developed in recent years for understating the relation between the 3D conformation of the genome and the phenotypes of cells in normal condition and diseases. In this review, we will discuss novel approaches for analyzing and modeling the 3D genomic conformation, focusing on deciphering disease-causing mutations that affect gene expression. We conclude that as this is a very challenging mission, an important direction should involve the comparative analysis of various 3D models from various organisms or cells.

Storage, visualization, and navigation of 3D genomics data

The field of 3D genomics grew at increasing rates in the last decade. The volume and complexity of 2D and 3D data produced is progressively outpacing the capacities of the technology previously used for distributing genome sequences. The emergence of new technologies provides also novel opportunities for the development of innovative approaches. In this paper, we review the state-of-the-art computing technology, as well as the solutions adopted by the platforms currently available.

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.

miniMDS: 3D structural inference from high-resolution Hi-C data

Motivation

Recent experiments have provided Hi-C data at resolution as high as 1 kbp. However, 3D structural inference from high-resolution Hi-C datasets is often computationally unfeasible using existing methods.

Results

We have developed miniMDS, an approximation of multidimensional scaling (MDS) that partitions a Hi-C dataset, performs high-resolution MDS separately on each partition, and then reassembles the partitions using low-resolution MDS. miniMDS is faster, more accurate, and uses less memory than existing methods for inferring the human genome at high resolution (10 kbp).

Availability and implementation

A Python implementation of miniMDS is available on GitHub: https://github.com/seqcode/miniMDS.

Supplementary information

Supplementary data are available at Bioinformatics online.

Computational 3D genome modeling using Chrom3D

Chrom3D is a computational platform for 3D genome modeling that simulates the spatial positioning of chromosome domains relative to each other and relative to the nuclear periphery. In Chrom3D, chromosomes are modeled as chains of contiguous beads, in which each bead represents a genomic domain. In this protocol, a bead represents a topologically associated domain (TAD) mapped from ensemble Hi-C data. Chrom3D takes as input data significant pairwise TAD-TAD interactions determined from a Hi-C contact matrix, and TAD interactions with the nuclear periphery, determined by ChIP-sequencing of nuclear lamins to define lamina-associated domains (LADs). Chrom3D is based on Monte Carlo simulations initiated from a starting random bead configuration. During the optimization process, TAD-TAD interactions constrain bead positions relative to each other, whereas LAD information constrains the corresponding bead toward the nuclear periphery. Optimization can be repeated many times to generate an ensemble of 3D genome models. Analyses of the models enable estimations of the radial positioning of genomic sites in the nucleus across cells in a population. Chrom3D provides opportunities to reveal spatial relationships between TADs and LADs. More generally, predictions from Chrom3D models can be experimentally tested in the laboratory. We describe the entire Chrom3D protocol for modeling a 3D diploid human genome, from the creation of input files to the final rendering of 3D genome structures. The procedure takes ∼18 h. Chrom3D is freely available on GitHub.

Producing genome structure populations with the dynamic and automated PGS software

Chromosome conformation capture technologies such as Hi-C are widely used to investigate the spatial organization of genomes. Because genome structures can vary considerably between individual cells of a population, interpreting ensemble-averaged Hi-C data can be challenging, in particular for long-range and interchromosomal interactions. We pioneered a probabilistic approach for the generation of a population of distinct diploid 3D genome structures consistent with all the chromatin-chromatin interaction probabilities from Hi-C experiments. Each structure in the population is a physical model of the genome in 3D. Analysis of these models yields new insights into the causes and the functional properties of the genome's organization in space and time. We provide a user-friendly software package, called PGS, which runs on local machines (for practice runs) and high-performance computing platforms. PGS takes a genome-wide Hi-C contact frequency matrix, along with information about genome segmentation, and produces an ensemble of 3D genome structures entirely consistent with the input. The software automatically generates an analysis report, and provides tools to extract and analyze the 3D coordinates of specific domains. Basic Linux command-line knowledge is sufficient for using this software. A typical running time of the pipeline is ∼3 d with 300 cores on a computer cluster to generate a population of 1,000 diploid genome structures at topological-associated domain (TAD)-level resolution.

A maximum likelihood algorithm for reconstructing 3D structures of human chromosomes from chromosomal contact data

Background

The development of chromosomal conformation capture techniques, particularly, the Hi-C technique, has made the analysis and study of the spatial conformation of a genome an important topic in bioinformatics and computational biology. Aided by high-throughput next generation sequencing techniques, the Hi-C technique can generate genome-wide, large-scale intra- and inter-chromosomal interaction data capable of describing in details the spatial interactions within a genome. These data can be used to reconstruct 3D structures of chromosomes that can be used to study DNA replication, gene regulation, genome interaction, genome folding, and genome function.

Results

Here, we introduce a maximum likelihood algorithm called 3DMax to construct the 3D structure of a chromosome from Hi-C data. 3DMax employs a maximum likelihood approach to infer the 3D structures of a chromosome, while automatically re-estimating the conversion factor (α) for converting Interaction Frequency (IF) to distance. Our results show that the models generated by 3DMax from a simulated Hi-C dataset match the true models better than most of the existing methods. 3DMax is more robust to structural variability and noise. Compared on a real Hi-C dataset, 3DMax constructs chromosomal models that fit the data better than most methods, and it is faster than all other methods. The models reconstructed by 3DMax were consistent with fluorescent in situ hybridization (FISH) experiments and existing knowledge about the organization of human chromosomes, such as chromosome compartmentalization.

Conclusions

3DMax is an effective approach to reconstructing 3D chromosomal models. The results, and the models generated for the simulated and real Hi-C datasets are available here: http://sysbio.rnet.missouri.edu/bdm_download/3DMax/. The source code is available here: https://github.com/BDM-Lab/3DMax. A short video demonstrating how to use 3DMax can be found here: https://youtu.be/ehQUFWoHwfo.

3D genome structure modeling by Lorentzian objective function

The 3D structure of the genome plays a vital role in biological processes such as gene interaction, gene regulation, DNA replication and genome methylation. Advanced chromosomal conformation capture techniques, such as Hi-C and tethered conformation capture, can generate chromosomal contact data that can be used to computationally reconstruct 3D structures of the genome. We developed a novel restraint-based method that is capable of reconstructing 3D genome structures utilizing both intra-and inter-chromosomal contact data. Our method was robust to noise and performed well in comparison with a panel of existing methods on a controlled simulated data set. On a real Hi-C data set of the human genome, our method produced chromosome and genome structures that are consistent with 3D FISH data and known knowledge about the human chromosome and genome, such as, chromosome territories and the cluster of small chromosomes in the nucleus center with the exception of the chromosome 18. The tool and experimental data are available at https://missouri.box.com/v/LorDG.

Integrative modelling of cellular assemblies

A wide variety of experimental techniques can be used for understanding the precise molecular mechanisms underlying the activities of cellular assemblies. The inherent limitations of a single experimental technique often requires integration of data from complementary approaches to gain sufficient insights into the assembly structure and function. Here, we review popular computational approaches for integrative modelling of cellular assemblies, including protein complexes and genomic assemblies. We provide recent examples of integrative models generated for such assemblies by different experimental techniques, especially including data from 3D electron microscopy (3D-EM) and chromosome conformation capture experiments, respectively. We highlight general concepts in integrative modelling and discuss the need for careful formulation and merging of different types of information.

Automatic analysis and 3D-modelling of Hi-C data using TADbit reveals structural features of the fly chromatin colors

The sequence of a genome is insufficient to understand all genomic processes carried out in the cell nucleus. To achieve this, the knowledge of its three-dimensional architecture is necessary. Advances in genomic technologies and the development of new analytical methods, such as Chromosome Conformation Capture (3C) and its derivatives, provide unprecedented insights in the spatial organization of genomes. Here we present TADbit, a computational framework to analyze and model the chromatin fiber in three dimensions. Our package takes as input the sequencing reads of 3C-based experiments and performs the following main tasks: (i) pre-process the reads, (ii) map the reads to a reference genome, (iii) filter and normalize the interaction data, (iv) analyze the resulting interaction matrices, (v) build 3D models of selected genomic domains, and (vi) analyze the resulting models to characterize their structural properties. To illustrate the use of TADbit, we automatically modeled 50 genomic domains from the fly genome revealing differential structural features of the previously defined chromatin colors, establishing a link between the conformation of the genome and the local chromatin composition. TADbit provides three-dimensional models built from 3C-based experiments, which are ready for visualization and for characterizing their relation to gene expression and epigenetic states. TADbit is an open-source Python library available for download from https://github.com/3DGenomes/tadbit.

Chrom3D: three-dimensional genome modeling from Hi-C and nuclear lamin-genome contacts

Current three-dimensional (3D) genome modeling platforms are limited by their inability to account for radial placement of loci in the nucleus. We present Chrom3D, a user-friendly whole-genome 3D computational modeling framework that simulates positions of topologically-associated domains (TADs) relative to each other and to the nuclear periphery. Chrom3D integrates chromosome conformation capture (Hi-C) and lamin-associated domain (LAD) datasets to generate structure ensembles that recapitulate radial distributions of TADs detected in single cells. Chrom3D reveals unexpected spatial features of LAD regulation in cells from patients with a laminopathy-causing lamin mutation. Chrom3D is freely available on github.

An integrated 3-Dimensional Genome Modeling Engine for data-driven simulation of spatial genome organization

ChIA-PET is a high-throughput mapping technology that reveals long-range chromatin interactions and provides insights into the basic principles of spatial genome organization and gene regulation mediated by specific protein factors. Recently, we showed that a single ChIA-PET experiment provides information at all genomic scales of interest, from the high-resolution locations of binding sites and enriched chromatin interactions mediated by specific protein factors, to the low resolution of nonenriched interactions that reflect topological neighborhoods of higher-order chromosome folding. This multilevel nature of ChIA-PET data offers an opportunity to use multiscale 3D models to study structural-functional relationships at multiple length scales, but doing so requires a structural modeling platform. Here, we report the development of 3D-GNOME (3-Dimensional Genome Modeling Engine), a complete computational pipeline for 3D simulation using ChIA-PET data. 3D-GNOME consists of three integrated components: a graph-distance-based heat map normalization tool, a 3D modeling platform, and an interactive 3D visualization tool. Using ChIA-PET and Hi-C data derived from human B-lymphocytes, we demonstrate the effectiveness of 3D-GNOME in building 3D genome models at multiple levels, including the entire genome, individual chromosomes, and specific segments at megabase (Mb) and kilobase (kb) resolutions of single average and ensemble structures. Further incorporation of CTCF-motif orientation and high-resolution looping patterns in 3D simulation provided additional reliability of potential biologically plausible topological structures.

Three-dimensional reconstruction of single-cell chromosome structure using recurrence plots

Single-cell analysis of the three-dimensional (3D) chromosome structure can reveal cell-to-cell variability in genome activities. Here, we propose to apply recurrence plots, a mathematical method of nonlinear time series analysis, to reconstruct the 3D chromosome structure of a single cell based on information of chromosomal contacts from genome-wide chromosome conformation capture (Hi-C) data. This recurrence plot-based reconstruction (RPR) method enables rapid reconstruction of a unique structure in single cells, even from incomplete Hi-C information.

Shape Transitions and Chiral Symmetry Breaking in the Energy Landscape of the Mitotic Chromosome

We derive an unbiased information theoretic energy landscape for chromosomes at metaphase using a maximum entropy approach that accurately reproduces the details of the experimentally measured pairwise contact probabilities between genomic loci. Dynamical simulations using this landscape lead to cylindrical, helically twisted structures reflecting liquid crystalline order. These structures are similar to those arising from a generic ideal homogenized chromosome energy landscape. The helical twist can be either right or left handed so chiral symmetry is broken spontaneously. The ideal chromosome landscape when augmented by interactions like those leading to topologically associating domain formation in the interphase chromosome reproduces these behaviors. The phase diagram of this landscape shows that the helical fiber order and the cylindrical shape persist at temperatures above the onset of chiral symmetry breaking, which is limited by the topologically associating domain interaction strength.

3D-GNOME: an integrated web service for structural modeling of the 3D genome

Recent advances in high-throughput chromosome conformation capture (3C) technology, such as Hi-C and ChIA-PET, have demonstrated the importance of 3D genome organization in development, cell differentiation and transcriptional regulation. There is now a widespread need for computational tools to generate and analyze 3D structural models from 3C data. Here we introduce our 3D GeNOme Modeling Engine (3D-GNOME), a web service which generates 3D structures from 3C data and provides tools to visually inspect and annotate the resulting structures, in addition to a variety of statistical plots and heatmaps which characterize the selected genomic region. Users submit a bedpe (paired-end BED format) file containing the locations and strengths of long range contact points, and 3D-GNOME simulates the structure and provides a convenient user interface for further analysis. Alternatively, a user may generate structures using published ChIA-PET data for the GM12878 cell line by simply specifying a genomic region of interest. 3D-GNOME is freely available at http://3dgnome.cent.uw.edu.pl/.

Simulated binding of transcription factors to active and inactive regions folds human chromosomes into loops, rosettes and topological domains

Biophysicists are modeling conformations of interphase chromosomes, often basing the strengths of interactions between segments distant on the genetic map on contact frequencies determined experimentally. Here, instead, we develop a fitting-free, minimal model: bivalent or multivalent red and green 'transcription factors' bind to cognate sites in strings of beads ('chromatin') to form molecular bridges stabilizing loops. In the absence of additional explicit forces, molecular dynamic simulations reveal that bound factors spontaneously cluster-red with red, green with green, but rarely red with green-to give structures reminiscent of transcription factories. Binding of just two transcription factors (or proteins) to active and inactive regions of human chromosomes yields rosettes, topological domains and contact maps much like those seen experimentally. This emergent 'bridging-induced attraction' proves to be a robust, simple and generic force able to organize interphase chromosomes at all scales.