Inferential modeling of 3D chromatin structure

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

Cohesin and CTCF complexes mediate contacts in chromatin loops depending on nucleosome positions

The spatial organization of the eukaryotic genome plays an important role in regulating transcriptional activity. In the nucleus, chromatin forms loops that assemble into fundamental units called topologically associating domains that facilitate or inhibit long-range contacts. These loops are formed and held together by the ring-shaped cohesin protein complex, and this can involve binding of CCCTC-binding factor (CTCF). High-resolution conformation capture experiments provide the frequency at which two DNA fragments physically associate in three-dimensional space. However, technical limitations of this approach, such as low throughput, low resolution, or noise in contact maps, make data interpretation and identification of chromatin intraloop contacts, e.g., between distal regulatory elements and their target genes, challenging. Herein, an existing coarse-grained model of chromatin at single-nucleosome resolution was extended by integrating potentials describing CTCF and cohesin. We performed replica-exchange Monte Carlo simulations with regularly spaced nucleosomes and experimentally determined nucleosome positions in the presence of cohesin-CTCF, as well as depleted systems as controls. In fully extruded loops caused by the presence of cohesin and CTCF, the number of contacts within the formed loops was increased. The number and types of these contacts were impacted by the nucleosome distribution and loop size. Microloops were observed within cohesin-mediated loops due to thermal fluctuations without additional influence of other factors, and the number, size, and shape of microloops were determined by nucleosome distribution and loop size. Nucleosome positions directly affect the spatial structure and contact probability within a loop, with presumed consequences for transcriptional activity.

ParticleChromo3D: a Particle Swarm Optimization algorithm for chromosome 3D structure prediction from Hi-C data

Background

The three-dimensional (3D) structure of chromatin has a massive effect on its function. Because of this, it is desirable to have an understanding of the 3D structural organization of chromatin. To gain greater insight into the spatial organization of chromosomes and genomes and the functions they perform, chromosome conformation capture (3C) techniques, particularly Hi-C, have been developed. The Hi-C technology is widely used and well-known because of its ability to profile interactions for all read pairs in an entire genome. The advent of Hi-C has greatly expanded our understanding of the 3D genome, genome folding, gene regulation and has enabled the development of many 3D chromosome structure reconstruction methods.

Results

Here, we propose a novel approach for 3D chromosome and genome structure reconstruction from Hi-C data using Particle Swarm Optimization (PSO) approach called ParticleChromo3D. This algorithm begins with a grouping of candidate solution locations for each chromosome bin, according to the particle swarm algorithm, and then iterates its position towards a global best candidate solution. While moving towards the optimal global solution, each candidate solution or particle uses its own local best information and a randomizer to choose its path. Using several metrics to validate our results, we show that ParticleChromo3D produces a robust and rigorous representation of the 3D structure for input Hi-C data. We evaluated our algorithm on simulated and real Hi-C data in this work. Our results show that ParticleChromo3D is more accurate than most of the existing algorithms for 3D structure reconstruction.

Conclusions

Our results also show that constructed ParticleChromo3D structures are very consistent, hence indicating that it will always arrive at the global solution at every iteration. The source code for ParticleChromo3D, the simulated and real Hi-C datasets, and the models generated for these datasets are available here: https://github.com/OluwadareLab/ParticleChromo3D

On the robustness of machine learning algorithms toward microfluidic distortions for cell classification via on-chip fluorescence microscopy

Single-cell imaging and sorting are critical technologies in biology and clinical applications. The power of these technologies is increased when combined with microfluidics, fluorescence markers, and machine learning. However, this quest faces several challenges. One of these is the effect of the sample flow velocity on the classification performances. Indeed, cell flow speed affects the quality of image acquisition by increasing motion blur and decreasing the number of acquired frames per sample. We investigate how these visual distortions impact the final classification task in a real-world use-case of cancer cell screening, using a microfluidic platform in combination with light sheet fluorescence microscopy. We demonstrate, by analyzing both simulated and experimental data, that it is possible to achieve high flow speed and high accuracy in single-cell classification. We prove that it is possible to overcome the 3D slice variability of the acquired 3D volumes, by relying on their 2D sum z-projection transformation, to reach an efficient real time classification with an accuracy of 99.4% using a convolutional neural network with transfer learning from simulated data. Beyond this specific use-case, we provide a web platform to generate a synthetic dataset and to investigate the effect of flow speed on cell classification for any biological samples and a large variety of fluorescence microscopes (https://www.creatis.insa-lyon.fr/site7/en/MicroVIP).

Uncovering the Principles of Genome Folding by 3D Chromatin Modeling

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

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

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

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

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.

The 3D Genome: From Structure to Function

The genome is the most functional part of a cell, and genomic contents are organized in a compact three-dimensional (3D) structure. The genome contains millions of nucleotide bases organized in its proper frame. Rapid development in genome sequencing and advanced microscopy techniques have enabled us to understand the 3D spatial organization of the genome. Chromosome capture methods using a ligation approach and the visualization tool of a 3D genome browser have facilitated detailed exploration of the genome. Topologically associated domains (TADs), lamin-associated domains, CCCTC-binding factor domains, cohesin, and chromatin structures are the prominent identified components that encode the 3D structure of the genome. Although TADs are the major contributors to 3D genome organization, they are absent in Arabidopsis. However, a few research groups have reported the presence of TAD-like structures in the plant kingdom.

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.

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.

Improving axial resolution in Structured Illumination Microscopy using deep learning

Structured Illumination Microscopy (SIM) is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy. Using recent advances in image up-scaling through deep learning models, we demonstrate a method to reconstruct 3D SIM image stacks with twice the axial resolution attainable through conventional SIM reconstructions. We further demonstrate our method is robust to noise and evaluate it against two-point cases and axial gratings. Finally, we discuss potential adaptions of the method to further improve resolution. This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 1)'.

Application of Hi-C and other omics data analysis in human cancer and cell differentiation research

With the development of 3C (chromosome conformation capture) and its derivative technology Hi-C (High-throughput chromosome conformation capture) research, the study of the spatial structure of the genomic sequence in the nucleus helps researchers understand the functions of biological processes such as gene transcription, replication, repair, and regulation. In this paper, we first introduce the research background and purpose of Hi-C data visualization analysis. After that, we discuss the Hi-C data analysis methods from genome 3D structure, A/B compartment, TADs (topologically associated domain), and loop detection. We also discuss how to apply genome visualization technologies to the identification of chromosome feature structures. We continue with a review of correlation analysis differences among multi-omics data, and how to apply Hi-C and other omics data analysis into cancer and cell differentiation research. Finally, we summarize the various problems in joint analyses based on Hi-C and other multi-omics data. We believe this review can help researchers better understand the progress and applications of 3D genome technology.

High-resolution single-cell 3D-models of chromatin ensembles during Drosophila embryogenesis

Single-cell chromatin studies provide insights into how chromatin structure relates to functions of individual cells. However, balancing high-resolution and genome wide-coverage remains challenging. We describe a computational method for the reconstruction of large 3D-ensembles of single-cell (sc) chromatin conformations from population Hi-C that we apply to study embryogenesis in Drosophila. With minimal assumptions of physical properties and without adjustable parameters, our method generates large ensembles of chromatin conformations via deep-sampling. Our method identifies specific interactions, which constitute 5-6% of Hi-C frequencies, but surprisingly are sufficient to drive chromatin folding, giving rise to the observed Hi-C patterns. Modeled sc-chromatins quantify chromatin heterogeneity, revealing significant changes during embryogenesis. Furthermore, >50% of modeled sc-chromatin maintain topologically associating domains (TADs) in early embryos, when no population TADs are perceptible. Domain boundaries become fixated during development, with strong preference at binding-sites of insulator-complexes upon the midblastula transition. Overall, high-resolution 3D-ensembles of sc-chromatin conformations enable further in-depth interpretation of population Hi-C, improving understanding of the structure-function relationship of genome organization.

ASHIC: hierarchical Bayesian modeling of diploid chromatin contacts and structures

The recently developed Hi-C technique has been widely applied to map genome-wide chromatin interactions. However, current methods for analyzing diploid Hi-C data cannot fully distinguish between homologous chromosomes. Consequently, the existing diploid Hi-C analyses are based on sparse and inaccurate allele-specific contact matrices, which might lead to incorrect modeling of diploid genome architecture. Here we present ASHIC, a hierarchical Bayesian framework to model allele-specific chromatin organizations in diploid genomes. We developed two models under the Bayesian framework: the Poisson-multinomial (ASHIC-PM) model and the zero-inflated Poisson-multinomial (ASHIC-ZIPM) model. The proposed ASHIC methods impute allele-specific contact maps from diploid Hi-C data and simultaneously infer allelic 3D structures. Through simulation studies, we demonstrated that ASHIC methods outperformed existing approaches, especially under low coverage and low SNP density conditions. Additionally, in the analyses of diploid Hi-C datasets in mouse and human, our ASHIC-ZIPM method produced fine-resolution diploid chromatin maps and 3D structures and provided insights into the allelic chromatin organizations and functions. To summarize, our work provides a statistically rigorous framework for investigating fine-scale allele-specific chromatin conformations. The ASHIC software is publicly available at https://github.com/wmalab/ASHIC.

Network-based method for regions with statistically frequent interchromosomal interactions at single-cell resolution

BACKGROUND

Chromosome conformation capture-based methods, especially Hi-C, enable scientists to detect genome-wide chromatin interactions and study the spatial organization of chromatin, which plays important roles in gene expression regulation, DNA replication and repair etc. Thus, developing computational methods to unravel patterns behind the data becomes critical. Existing computational methods focus on intrachromosomal interactions and ignore interchromosomal interactions partly because there is no prior knowledge for interchromosomal interactions and the frequency of interchromosomal interactions is much lower while the search space is much larger. With the development of single-cell technologies, the advent of single-cell Hi-C makes interrogating the spatial structure of chromatin at single-cell resolution possible. It also brings a new type of frequency information, the number of single cells with chromatin interactions between two disjoint chromosome regions.

RESULTS

Considering the lack of computational methods on interchromosomal interactions and the unsurprisingly frequent intrachromosomal interactions along the diagonal of a chromatin contact map, we propose a computational method dedicated to analyzing interchromosomal interactions of single-cell Hi-C with this new frequency information. To the best of our knowledge, our proposed tool is the first to identify regions with statistically frequent interchromosomal interactions at single-cell resolution. We demonstrate that the tool utilizing networks and binomial statistical tests can identify interesting structural regions through visualization, comparison and enrichment analysis and it also supports different configurations to provide users with flexibility.

CONCLUSIONS

It will be a useful tool for analyzing single-cell Hi-C interchromosomal interactions.

GSDB: a database of 3D chromosome and genome structures reconstructed from Hi-C data

Advances in the study of chromosome conformation capture technologies, such as Hi-C technique - capable of capturing chromosomal interactions in a genome-wide scale - have led to the development of three-dimensional chromosome and genome structure reconstruction methods from Hi-C data. The three dimensional genome structure is important because it plays a role in a variety of important biological activities such as DNA replication, gene regulation, genome interaction, and gene expression. In recent years, numerous Hi-C datasets have been generated, and likewise, a number of genome structure construction algorithms have been developed.

In this work, we outline the construction of a novel Genome Structure Database (GSDB) to create a comprehensive repository that contains 3D structures for Hi-C datasets constructed by a variety of 3D structure reconstruction tools. The GSDB contains over 50,000 structures from 12 state-of-the-art Hi-C data structure prediction algorithms for 32 Hi-C datasets.

GSDB functions as a centralized collection of genome structures which will enable the exploration of the dynamic architectures of chromosomes and genomes for biomedical research. GSDB is accessible at http://sysbio.rnet.missouri.edu/3dgenome/GSDB

Bayesian inference of chromatin structure ensembles from population-averaged contact data

Mounting experimental evidence suggests a role for the spatial organization of chromatin in crucial processes of the cell nucleus such as transcription regulation. Chromosome conformation capture techniques allow us to characterize chromatin structure by mapping contacts between chromosomal loci on a genome-wide scale. The most widespread modality is to measure contact frequencies averaged over a population of cells. Single-cell variants exist, but suffer from low contact numbers and have not yet gained the same resolution as population methods. While intriguing biological insights have already been garnered from ensemble-averaged data, information about three-dimensional (3D) genome organization in the underlying individual cells remains largely obscured because the contact maps show only an average over a huge population of cells. Moreover, computational methods for structure modeling of chromatin have mostly focused on fitting a single consensus structure, thereby ignoring any cell-to-cell variability in the model itself. Here, we propose a fully Bayesian method to infer ensembles of chromatin structures and to determine the optimal number of states in a principled, objective way. We illustrate our approach on simulated data and compute multistate models of chromatin from chromosome conformation capture carbon copy (5C) data. Comparison with independent data suggests that the inferred ensembles represent the underlying sample population faithfully. Harnessing the rich information contained in multistate models, we investigate cell-to-cell variability of chromatin organization into topologically associating domains, thus highlighting the ability of our approach to deliver insights into chromatin organization of great biological relevance.

Joint inference and alignment of genome structures enables characterization of compartment-independent reorganization across cell types

BACKGROUND

Comparisons of Hi-C data sets between cell types and conditions have revealed differences in topologically associated domains (TADs) and A/B compartmentalization, which are correlated with differences in gene regulation. However, previous comparisons have focused on known forms of 3D organization while potentially neglecting other functionally relevant differences. We aimed to create a method to quantify all locus-specific differences between two Hi-C data sets.

RESULTS

We developed MultiMDS to jointly infer and align 3D chromosomal structures from two Hi-C data sets, thereby enabling a new way to comprehensively quantify relocalization of genomic loci between cell types. We demonstrate this approach by comparing Hi-C data across a variety of cell types. We consistently find relocalization of loci with minimal difference in A/B compartment score. For example, we identify compartment-independent relocalizations between GM12878 and K562 cells that involve loci displaying enhancer-associated histone marks in one cell type and polycomb-associated histone marks in the other.

CONCLUSIONS

MultiMDS is the first tool to identify all loci that relocalize between two Hi-C data sets. Our method can identify 3D localization differences that are correlated with cell-type-specific regulatory activities and which cannot be identified using other methods.

Reconstructing spatial organizations of chromosomes through manifold learning

Decoding the spatial organizations of chromosomes has crucial implications for studying eukaryotic gene regulation. Recently, chromosomal conformation capture based technologies, such as Hi-C, have been widely used to uncover the interaction frequencies of genomic loci in a high-throughput and genome-wide manner and provide new insights into the folding of three-dimensional (3D) genome structure. In this paper, we develop a novel manifold learning based framework, called GEM (Genomic organization reconstructor based on conformational Energy and Manifold learning), to reconstruct the three-dimensional organizations of chromosomes by integrating Hi-C data with biophysical feasibility. Unlike previous methods, which explicitly assume specific relationships between Hi-C interaction frequencies and spatial distances, our model directly embeds the neighboring affinities from Hi-C space into 3D Euclidean space. Extensive validations demonstrated that GEM not only greatly outperformed other state-of-art modeling methods but also provided a physically and physiologically valid 3D representations of the organizations of chromosomes. Furthermore, we for the first time apply the modeled chromatin structures to recover long-range genomic interactions missing from original Hi-C 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.

Integrating Hi-C and FISH data for modeling of the 3D organization of chromosomes

The new advances in various experimental techniques that provide complementary information about the spatial conformations of chromosomes have inspired researchers to develop computational methods to fully exploit the merits of individual data sources and combine them to improve the modeling of chromosome structure. Here we propose GEM-FISH, a method for reconstructing the 3D models of chromosomes through systematically integrating both Hi-C and FISH data with the prior biophysical knowledge of a polymer model. Comprehensive tests on a set of chromosomes, for which both Hi-C and FISH data are available, demonstrate that GEM-FISH can outperform previous chromosome structure modeling methods and accurately capture the higher order spatial features of chromosome conformations. Moreover, our reconstructed 3D models of chromosomes revealed interesting patterns of spatial distributions of super-enhancers which can provide useful insights into understanding the functional roles of these super-enhancers in gene regulation.

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.

Chromosome territories and the global regulation of the genome

Spatial positioning is a fundamental principle governing nuclear processes. Chromatin is organized as a hierarchy from nucleosomes to Mbp chromatin domains (CD) or topologically associating domains (TADs) to higher level compartments culminating in chromosome territories (CT). Microscopic and sequencing techniques have substantiated chromatin organization as a critical factor regulating gene expression. For example, enhancers loop back to interact with their target genes almost exclusively within TADs, distally located coregulated genes reposition into common transcription factories upon activation, and Mbp CDs exhibit dynamic motion and configurational changes in vivo. A longstanding question in the nucleus field is whether an interactive nuclear matrix provides a direct link between structure and function. The findings of nonrandom radial positioning of CT within the nucleus suggest the possibility of preferential interaction patterns among populations of CT. Sequential labeling up to 10 CT followed by application of computer imaging and geometric graph mining algorithms revealed cell-type specific interchromosomal networks (ICN) of CT that are altered during the cell cycle, differentiation, and cancer progression. It is proposed that the ICN correlate with the global level of genome regulation. These approaches also demonstrated that the large scale 3-D topology of CT is specific for each CT. The cell-type specific proximity of certain chromosomal regions in normal cells may explain the propensity of distinct translocations in cancer subtypes. Understanding how genes are dysregulated upon disruption of the normal "wiring" of the nucleus by translocations, deletions, and amplifications that are hallmarks of cancer, should enable more targeted therapeutic strategies.

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.

Computational methods for analyzing and modeling genome structure and organization

Recent advances in chromosome conformation capture technologies have led to the discovery of previously unappreciated structural features of chromatin. Computational analysis has been critical in detecting these features and thereby helping to uncover the building blocks of genome architecture. Algorithms are being developed to integrate these architectural features to construct better three-dimensional (3D) models of the genome. These computational methods have revealed the importance of 3D genome organization to essential biological processes. In this article, we review the state of the art in analytic and modeling techniques with a focus on their application to answering various biological questions related to chromatin structure. We summarize the limitations of these computational techniques and suggest future directions, including the importance of incorporating multiple sources of experimental data in building a more comprehensive model of the genome. This article is categorized under: Analytical and Computational Methods > Computational Methods Laboratory Methods and Technologies > Genetic/Genomic Methods Models of Systems Properties and Processes > Mechanistic Models.

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.

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.

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.

3D Genome Reconstruction with ShRec3D+ and Hi-C Data

Hi-C technology, a chromosome conformation capture (3C) based method, has been developed to capture genome-wide interactions at a given resolution. The next challenge is to reconstruct 3D structure of genome from the 3C-derived data computationally. Several existing methods have been proposed to obtain a consensus structure or ensemble structures. These methods can be categorized as probabilistic models or restraint-based models. In this paper, we propose a method, named ShRec3D+, to infer a consensus 3D structure of a genome from Hi-C data. The method is a two-step algorithm which is based on ChromSDE and ShRec3D methods. First, correct the conversion factor by golden section search for converting interaction frequency data to a distance weighted graph. Second, apply shortest-path algorithm and multi-dimensional scaling (MDS) algorithm to compute the 3D coordinates of a set of genomic loci from the distance graph. We validate ShRec3D+ accuracy on both simulation data and publicly Hi-C data. Our test results indicate that our method successfully corrects the parameter with a given resolution, is more accurate than ShRec3D, and is more efficient and robust than ChromSDE.

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.

Network analysis identifies chromosome intermingling regions as regulatory hotspots for transcription

We develop a network analysis approach for identifying clusters of interactions between chromosomes, which we validate experimentally. Our method integrates 1D features of the genome, such as epigenetic marks, with 3D interactions, allowing us to study spatially colocalized regions between chromosomes that are functionally relevant. We observe that clusters of interchromosomal regions fall into active and inactive categories. We find that active clusters share transcription factors and are enriched for transcriptional machinery, suggesting that chromosome intermingling regions play a key role in genome regulation. Our method provides a unique quantitative framework that can be broadly applied to study the principles of genome organization and regulation during processes such as cell differentiation and reprogramming.

The 3D structure of the genome plays a key role in regulatory control of the cell. Experimental methods such as high-throughput chromosome conformation capture (Hi-C) have been developed to probe the 3D structure of the genome. However, it remains a challenge to deduce from these data chromosome regions that are colocalized and coregulated. Here, we present an integrative approach that leverages 1D functional genomic features (e.g., epigenetic marks) with 3D interactions from Hi-C data to identify functional interchromosomal interactions. We construct a weighted network with 250-kb genomic regions as nodes and Hi-C interactions as edges, where the edge weights are given by the correlation between 1D genomic features. Individual interacting clusters are determined using weighted correlation clustering on the network. We show that intermingling regions generally fall into either active or inactive clusters based on the enrichment for RNA polymerase II (RNAPII) and H3K9me3, respectively. We show that active clusters are hotspots for transcription factor binding sites. We also validate our predictions experimentally by 3D fluorescence in situ hybridization (FISH) experiments and show that active RNAPII is enriched in predicted active clusters. Our method provides a general quantitative framework that couples 1D genomic features with 3D interactions from Hi-C to probe the guiding principles that link the spatial organization of the genome with regulatory control.

Computational construction of 3D chromatin ensembles and prediction of functional interactions of alpha-globin locus from 5C data

Conformation capture technologies measure frequencies of interactions between chromatin regions. However, understanding gene-regulation require knowledge of detailed spatial structures of heterogeneous chromatin in cells. Here we describe the nC-SAC (n-Constrained-Self Avoiding Chromatin) method that transforms experimental interaction frequencies into 3D ensembles of chromatin chains. nC-SAC first distinguishes specific from non-specific interaction frequencies, then generates 3D chromatin ensembles using identified specific interactions as spatial constraints. Application to α-globin locus shows that these constraints (∼20%) drive the formation of ∼99% all experimentally captured interactions, in which ∼30% additional to the imposed constraints is found to be specific. Many novel specific spatial contacts not captured by experiments are also predicted. A subset, of which independent ChIA-PET data are available, is validated to be RNAPII-, CTCF-, and RAD21-mediated. Their positioning in the architectural context of imposed specific interactions from nC-SAC is highly important. Our results also suggest the presence of a many-body structural unit involving α-globin gene, its enhancers, and POL3RK gene for regulating the expression of α-globin in silent cells.

The three-dimensional genome organization of Drosophila melanogaster through data integration

BACKGROUND

Genome structures are dynamic and non-randomly organized in the nucleus of higher eukaryotes. To maximize the accuracy and coverage of three-dimensional genome structural models, it is important to integrate all available sources of experimental information about a genome's organization. It remains a major challenge to integrate such data from various complementary experimental methods. Here, we present an approach for data integration to determine a population of complete three-dimensional genome structures that are statistically consistent with data from both genome-wide chromosome conformation capture (Hi-C) and lamina-DamID experiments.

RESULTS

Our structures resolve the genome at the resolution of topological domains, and reproduce simultaneously both sets of experimental data. Importantly, this data deconvolution framework allows for structural heterogeneity between cells, and hence accounts for the expected plasticity of genome structures. As a case study we choose Drosophila melanogaster embryonic cells, for which both data types are available. Our three-dimensional genome structures have strong predictive power for structural features not directly visible in the initial data sets, and reproduce experimental hallmarks of the D. melanogaster genome organization from independent and our own imaging experiments. Also they reveal a number of new insights about genome organization and its functional relevance, including the preferred locations of heterochromatic satellites of different chromosomes, and observations about homologous pairing that cannot be directly observed in the original Hi-C or lamina-DamID data.

CONCLUSIONS

Our approach allows systematic integration of Hi-C and lamina-DamID data for complete three-dimensional genome structure calculation, while also explicitly considering genome structural variability.

Spatial organization of the budding yeast genome in the cell nucleus and identification of specific chromatin interactions from multi-chromosome constrained chromatin model

Nuclear landmarks and biochemical factors play important roles in the organization of the yeast genome. The interaction pattern of budding yeast as measured from genome-wide 3C studies are largely recapitulated by model polymer genomes subject to landmark constraints. However, the origin of inter-chromosomal interactions, specific roles of individual landmarks, and the roles of biochemical factors in yeast genome organization remain unclear. Here we describe a multi-chromosome constrained self-avoiding chromatin model (mC-SAC) to gain understanding of the budding yeast genome organization. With significantly improved sampling of genome structures, both intra- and inter-chromosomal interaction patterns from genome-wide 3C studies are accurately captured in our model at higher resolution than previous studies. We show that nuclear confinement is a key determinant of the intra-chromosomal interactions, and centromere tethering is responsible for the inter-chromosomal interactions. In addition, important genomic elements such as fragile sites and tRNA genes are found to be clustered spatially, largely due to centromere tethering. We uncovered previously unknown interactions that were not captured by genome-wide 3C studies, which are found to be enriched with tRNA genes, RNAPIII and TFIIS binding. Moreover, we identified specific high-frequency genome-wide 3C interactions that are unaccounted for by polymer effects under landmark constraints. These interactions are enriched with important genes and likely play biological roles.

The architecture of the cell nucleus and the spatial organization of the genome are important in determining nuclear functions. Single-cell imaging techniques and chromosome conformation capture (3C) based methods have provided a wealth of information on the spatial organization of chromosomes. Here we describe a multi-chromosome ensemble model of chromatin chains for understanding the folding principles of budding yeast genome. By overcoming severe challenges in sampling self-avoiding chromatin chains in nuclear confinement, we succeed in generating a large number of model genomes of budding yeast. Our model predicts chromatin interactions that have good correlation with experimental measurements. Our results showed that the spatial confinement of cell nucleus and excluded-volume effect are key determinants of the folding behavior of yeast chromosomes, and largely account for the observed intra-chromosomal interactions. Furthermore, we determined the specific roles of individual nuclear landmarks and biochemical factors, and our analysis showed that centromere tethering largely determines inter-chromosomal interactions. In addition, we were able to infer biological properties from the organization of modeled genomes. We found that the spatial locations of important elements such as fragile sites and tRNA genes are largely determined by the tethering of centromeres to the Spindle Pole Body. We further showed that many of these spatial locations can be predicted by using the genomic distances to the centromeres. Overall, our results revealed important insight into the organizational principles of the budding yeast genome and predicted a number of important biological findings that are fully experimentally testable.

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.

Inferential Structure Determination of Chromosomes from Single-Cell Hi-C Data

Chromosome conformation capture (3C) techniques have revealed many fascinating insights into the spatial organization of genomes. 3C methods typically provide information about chromosomal contacts in a large population of cells, which makes it difficult to draw conclusions about the three-dimensional organization of genomes in individual cells. Recently it became possible to study single cells with Hi-C, a genome-wide 3C variant, demonstrating a high cell-to-cell variability of genome organization. In principle, restraint-based modeling should allow us to infer the 3D structure of chromosomes from single-cell contact data, but suffers from the sparsity and low resolution of chromosomal contacts. To address these challenges, we adapt the Bayesian Inferential Structure Determination (ISD) framework, originally developed for NMR structure determination of proteins, to infer statistical ensembles of chromosome structures from single-cell data. Using ISD, we are able to compute structural error bars and estimate model parameters, thereby eliminating potential bias imposed by ad hoc parameter choices. We apply and compare different models for representing the chromatin fiber and for incorporating singe-cell contact information. Finally, we extend our approach to the analysis of diploid chromosome data.

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.

The folding landscape of the epigenome

The role of the spatial organization of chromatin in gene regulation is a long-standing but still open question. Experimentally it has been shown that the genome is segmented into epigenomic chromatin domains that are organized into hierarchical sub-nuclear spatial compartments. However, whether this non-random spatial organization only reflects or indeed contributes-and how-to the regulation of genome function remains to be elucidated. To address this question, we recently proposed a quantitative description of the folding properties of the fly genome as a function of its epigenomic landscape using a polymer model with epigenomic-driven attractions. We propose in this article, to characterize more deeply the physical properties of the 3D epigenome folding. Using an efficient lattice version of the original block copolymer model, we study the structural and dynamical properties of chromatin and show that the size of epigenomic domains and asymmetries in sizes and in interaction strengths play a critical role in the chromatin organization. Finally, we discuss the biological implications of our findings. In particular, our predictions are quantitatively compatible with experimental data and suggest a different mean of self-interaction in euchromatin versus heterochromatin domains.

Population-based 3D genome structure analysis reveals driving forces in spatial genome organization

Conformation capture technologies (e.g., Hi-C) chart physical interactions between chromatin regions on a genome-wide scale. However, the structural variability of the genome between cells poses a great challenge to interpreting ensemble-averaged Hi-C data, particularly for long-range and interchromosomal interactions. Here, we present a probabilistic approach for deconvoluting Hi-C data into a model population of distinct diploid 3D genome structures, which facilitates the detection of chromatin interactions likely to co-occur in individual cells. Our approach incorporates the stochastic nature of chromosome conformations and allows a detailed analysis of alternative chromatin structure states. For example, we predict and experimentally confirm the presence of large centromere clusters with distinct chromosome compositions varying between individual cells. The stability of these clusters varies greatly with their chromosome identities. We show that these chromosome-specific clusters can play a key role in the overall chromosome positioning in the nucleus and stabilizing specific chromatin interactions. By explicitly considering genome structural variability, our population-based method provides an important tool for revealing novel insights into the key factors shaping the spatial genome organization.

Large-scale probabilistic 3D organization of human chromosome territories

There is growing evidence that chromosome territories (CT) have a probabilistic non-random arrangement within the cell nucleus of mammalian cells including radial positioning and preferred patterns of interchromosomal interactions that are cell-type specific. While it is generally assumed that the three-dimensional (3D) arrangement of genes within the CT is linked to genomic regulation, the degree of non-random organization of individual CT remains unclear. As a first step to elucidating the global 3D organization (topology) of individual CT, we performed multi-color fluorescence in situ hybridization using six probes extending across each chromosome in human WI38 lung fibroblasts. Six CT were selected ranging in size and gene density (1, 4, 12, 17, 18 and X). In-house computational geometric algorithms were applied to measure the 3D distances between every combination of probes and to elucidate data-mined structural patterns. Our findings demonstrate a high degree of non-random arrangement of individual CT that vary from chromosome to chromosome and display distinct changes during the cell cycle. Application of a classic, well-defined data mining and pattern recognition approach termed the 'k-means' generated 3D models for the best fit arrangement of each chromosome. These predicted models correlated well with the detailed distance measurements and analysis. We propose that the unique 3D topology of each CT and characteristic changes during the cell cycle provide the structural framework for the global gene expression programs of the individual chromosomes.

Analysis methods for studying the 3D architecture of the genome

The rapidly increasing quantity of genome-wide chromosome conformation capture data presents great opportunities and challenges in the computational modeling and interpretation of the three-dimensional genome. In particular, with recent trends towards higher-resolution high-throughput chromosome conformation capture (Hi-C) data, the diversity and complexity of biological hypotheses that can be tested necessitates rigorous computational and statistical methods as well as scalable pipelines to interpret these datasets. Here we review computational tools to interpret Hi-C data, including pipelines for mapping, filtering, and normalization, and methods for confidence estimation, domain calling, visualization, and three-dimensional modeling.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

Genome sequences provide the overall genetic blueprint of cells, but cells possessing the same genome can exhibit diverse phenotypes. There is a multitude of mechanisms controlling cellular epigenetic states and that dictate the behavior of cells. Among these, networks of interacting molecules, often under stochastic control, depending on the specific wirings of molecular components and the physiological conditions, can have a different landscape of cellular states. In addition, chromosome folding in three-dimensional space provides another important control mechanism for selective activation and repression of gene expression. Fully differentiated cells with different properties grow, divide, and interact through mechanical forces and communicate through signal transduction, resulting in the formation of complex tissue patterns. Developing quantitative models to study these multi-scale phenomena and to identify opportunities for improving human health requires development of theoretical models, algorithms, and computational tools. Here we review recent progress made in these important directions.