Understanding spatial organizations of chromosomes via statistical analysis of Hi-C data

Chromatin remodeling analysis reveals the RdDM pathway responds to low-phosphorus stress in maize

Chromatin in eukaryotes folds into a complex three-dimensional (3D) structure that is essential for controlling gene expression and cellular function and is dynamically regulated in biological processes. Studies on plant phosphorus signaling have concentrated on single genes and gene interactions. It is critical to expand the existing signaling pathway in terms of its 3D structure. In this study, low-Pi treatment led to greater chromatin volume. Furthermore, low-Pi stress increased the insulation score and the number of TAD-like domains, but the effects on the A/B compartment were not obvious. The methylation levels of target sites (hereafter as RdDM levels) peaked at specific TAD-like boundaries, whereas RdDM peak levels at conserved TAD-like boundaries shifted and decreased sharply. The distribution pattern of RdDM sites originating from the Helitron transposons matched that of genome-wide RdDM sites near TAD-like boundaries. RdDM pathway genes were upregulated in the middle or early stages and downregulated in the later stages under low-Pi conditions. The RdDM pathway mutant ddm1a showed increased tolerance to low-Pi stress, with shortened and thickened roots contributing to higher Pi uptake from the shallow soil layer. ChIP-seq results revealed that ZmDDM1A could bind to Pi- and root development-related genes. Strong associations were found between interacting genes in significantly different chromatin-interaction regions and root traits. These findings not only expand the mechanisms by which plants respond to low-Pi stress through the RdDM pathway but also offer a crucial framework for the analysis of biological issues using 3D genomics.

LPAD: using network construction and label propagation to detect topologically associating domains from Hi-C data

With the development of chromosome conformation capture technique, the study of spatial conformation of a genome based on Hi-C technique has made a quantum leap. Previous studies reveal that genomes are folded into hierarchy of three-dimensional (3D) structures associated with topologically associating domains (TADs), and detecting TAD boundaries is of great significance in the chromosome-level analysis of 3D genome architecture. In this paper, we propose a novel TAD identification method, LPAD, which first extracts node correlations from global interactions of chromosomes based on the random walk with restart and then builds an undirected graph from Hi-C contact matrix. Next, LPAD designs a label propagation-based approach to discover communities and generates TADs. Experimental results verify the effectiveness and quality of TAD detections compared with existing methods. Furthermore, experimental evaluation of chromatin immunoprecipitation sequencing data shows that LPAD performs high enrichment of histone modifications remarkably nearby the TAD boundaries, and these results demonstrate LPAD's advantages on TAD identification accuracy.

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.

Exploring the 2D and 3D structural properties of topologically associating domains

BACKGROUND

Topologically associating domains (TADs) are genomic regions with varying lengths. The interactions within TADs are more frequent than those between different TADs. TADs or sub-TADs are considered the structural and functional units of the mammalian genomes. Although TADs are important for understanding how genomes function, we have limited knowledge about their 3D structural properties.

RESULTS

In this study, we designed and benchmarked three metrics for capturing the three-dimensional and two-dimensional structural signatures of TADs, which can help better understand TADs' structural properties and the relationships between structural properties and genetic and epigenetic features. The first metric for capturing 3D structural properties is radius of gyration, which in this study is used to measure the spatial compactness of TADs. The mass value of each DNA bead in a 3D structure is novelly defined as one or more genetic or epigenetic feature(s). The second metric is folding degree. The last metric is exponent parameter, which is used to capture the 2D structural properties based on TADs' Hi-C contact matrices. In general, we observed significant correlations between the three metrics and the genetic and epigenetic features. We made the same observations when using H3K4me3, transcription start sites, and RNA polymerase II to represent the mass value in the modified radius-of-gyration metric. Moreover, we have found that the TADs in the clusters of depleted chromatin states apparently correspond to smaller exponent parameters and larger radius of gyrations. In addition, a new objective function of multidimensional scaling for modelling chromatin or TADs 3D structures was designed and benchmarked, which can handle the DNA bead-pairs with zero Hi-C contact values.

CONCLUSIONS

The web server for reconstructing chromatin 3D structures using multiple different objective functions and the related source code are publicly available at http://dna.cs.miami.edu/3DChrom/.

Regulatory variants: from detection to predicting impact

Variants within non-coding genomic regions can greatly affect disease. In recent years, increasing focus has been given to these variants, and how they can alter regulatory elements, such as enhancers, transcription factor binding sites and DNA methylation regions. Such variants can be considered regulatory variants. Concurrently, much effort has been put into establishing international consortia to undertake large projects aimed at discovering regulatory elements in different tissues, cell lines and organisms, and probing the effects of genetic variants on regulation by measuring gene expression. Here, we describe methods and techniques for discovering disease-associated non-coding variants using sequencing technologies. We then explain the computational procedures that can be used for annotating these variants using the information from the aforementioned projects, and prediction of their putative effects, including potential pathogenicity, based on rule-based and machine learning approaches. We provide the details of techniques to validate these predictions, by mapping chromatin-chromatin and chromatin-protein interactions, and introduce Clustered Regularly Interspaced Short Palindromic Repeats-Associated Protein 9 (CRISPR-Cas9) technology, which has already been used in this field and is likely to have a big impact on its future evolution. We also give examples of regulatory variants associated with multiple complex diseases. This review is aimed at bioinformaticians interested in the characterization of regulatory variants, molecular biologists and geneticists interested in understanding more about the nature and potential role of such variants from a functional point of views, and clinicians who may wish to learn about variants in non-coding genomic regions associated with a given disease and find out what to do next to uncover how they impact on the underlying mechanisms.

RT States: systematic annotation of the human genome using cell type-specific replication timing programs

MOTIVATION

The replication timing (RT) program has been linked to many key biological processes including cell fate commitment, 3D chromatin organization and transcription regulation. Significant technology progress now allows to characterize the RT program in the entire human genome in a high-throughput and high-resolution fashion. These experiments suggest that RT changes dynamically during development in coordination with gene activity. Since RT is such a fundamental biological process, we believe that an effective quantitative profile of the local RT program from a diverse set of cell types in various developmental stages and lineages can provide crucial biological insights for a genomic locus.

RESULTS

In this study, we explored recurrent and spatially coherent combinatorial profiles from 42 RT programs collected from multiple lineages at diverse differentiation states. We found that a Hidden Markov Model with 15 hidden states provide a good model to describe these genome-wide RT profiling data. Each of the hidden state represents a unique combination of RT profiles across different cell types which we refer to as 'RT states'. To understand the biological properties of these RT states, we inspected their relationship with chromatin states, gene expression, functional annotation and 3D chromosomal organization. We found that the newly defined RT states possess interesting genome-wide functional properties that add complementary information to the existing annotation of the human genome.

AVAILABILITY AND IMPLEMENTATION

R scripts for inferring HMM models and Perl scripts for further analysis are available https://github.com/PouletAxel/script_HMM_Replication_timing.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Deciphering Hi-C: from 3D genome to function

Hi-C is a commonly used technology in 3D genomics which can depict global chromatin interactions across eukaryotic genome. Integrating with different datasets, it can also be applied to studying various biological questions, such as nuclear organization, gene transcription regulation, spatiotemporal development, genome assembly, and cancer genomics. During the last decade, the development and application of Hi-C have dramatically changed the view of genome architecture, chromatin conformation, and gene interaction. So far, Hi-C-related studies remain vivacious and controversial; thus, a unified standard of library construction and bioinformatics analysis are urgently needed. In this review, we have summarized its history, development, methodologies, advances, applications, shortages, and future perspectives. We discuss a few limitations of the current Hi-C technologies and future directions for improvement and highlight how Hi-C can bridge 3D structure to gene function. This review will be helpful for scientists who want to engage in the 3D genomics field; it also shows some future tracks.

3C and 3C-based techniques: the powerful tools for spatial genome organization deciphering

It is well known that the chromosomes are organized in the nucleus and this spatial arrangement of genome play a crucial role in gene regulation and genome stability. Different techniques have been developed and applied to uncover the intrinsic mechanism of genome architecture, especially the chromosome conformation capture (3C) and 3C-derived methods. 3C and 3C-derived techniques provide us approaches to perform high-throughput chromatin architecture assays at the genome scale. However, the advantage and disadvantage of current methodologies of C-technologies have not been discussed extensively. In this review, we described and compared the methodologies of C-technologies used in genome organization studies with an emphasis on Hi-C method. We also discussed the crucial challenges facing current genome architecture studies based on 3C and 3C-derived technologies and the direction of future technologies to address currently outstanding questions in the field. These latest news contribute to our current understanding of genome structure, and provide a comprehensive reference for researchers to choose the appropriate method in future application. We consider that these constantly improving technologies will offer a finer and more accurate contact profiles of entire genome and ultimately reveal specific molecular machines govern its shape and function.

Large-scale chromosome folding versus genomic DNA sequences: A discrete double Fourier transform technique

Using state-of-the-art techniques combining imaging methods and high-throughput genomic mapping tools leaded to the significant progress in detailing chromosome architecture of various organisms. However, a gap still remains between the rapidly growing structural data on the chromosome folding and the large-scale genome organization. Could a part of information on the chromosome folding be obtained directly from underlying genomic DNA sequences abundantly stored in the databanks? To answer this question, we developed an original discrete double Fourier transform (DDFT). DDFT serves for the detection of large-scale genome regularities associated with domains/units at the different levels of hierarchical chromosome folding. The method is versatile and can be applied to both genomic DNA sequences and corresponding physico-chemical parameters such as base-pairing free energy. The latter characteristic is closely related to the replication and transcription and can also be used for the assessment of temperature or supercoiling effects on the chromosome folding. We tested the method on the genome of E. coli K-12 and found good correspondence with the annotated domains/units established experimentally. As a brief illustration of further abilities of DDFT, the study of large-scale genome organization for bacteriophage PHIX174 and bacterium Caulobacter crescentus was also added. The combined experimental, modeling, and bioinformatic DDFT analysis should yield more complete knowledge on the chromosome architecture and genome organization.

Statistical challenges in analyzing methylation and long-range chromosomal interaction data

With the rapid development of high throughput technologies such as array and next generation sequencing (NGS), genome-wide, nucleotide-resolution epigenomic data are increasingly available. In recent years, there has been particular interest in data on DNA methylation and 3-dimensional (3D) chromosomal organization, which are believed to hold keys to understand biological mechanisms, such as transcription regulation, that are closely linked to human health and diseases. However, small sample size, complicated correlation structure, substantial noise, biases, and uncertainties, all present difficulties for performing statistical inference. In this review, we present an overview of the new technologies that are frequently utilized in studying DNA methylation and 3D chromosomal organization. We focus on reviewing recent developments in statistical methodologies designed for better interrogating epigenomic data, pointing out statistical challenges facing the field whenever appropriate.

Computational Identification of Genomic Features That Influence 3D Chromatin Domain Formation

Recent advances in long-range Hi-C contact mapping have revealed the importance of the 3D structure of chromosomes in gene expression. A current challenge is to identify the key molecular drivers of this 3D structure. Several genomic features, such as architectural proteins and functional elements, were shown to be enriched at topological domain borders using classical enrichment tests. Here we propose multiple logistic regression to identify those genomic features that positively or negatively influence domain border establishment or maintenance. The model is flexible, and can account for statistical interactions among multiple genomic features. Using both simulated and real data, we show that our model outperforms enrichment test and non-parametric models, such as random forests, for the identification of genomic features that influence domain borders. Using Drosophila Hi-C data at a very high resolution of 1 kb, our model suggests that, among architectural proteins, BEAF-32 and CP190 are the main positive drivers of 3D domain borders. In humans, our model identifies well-known architectural proteins CTCF and cohesin, as well as ZNF143 and Polycomb group proteins as positive drivers of domain borders. The model also reveals the existence of several negative drivers that counteract the presence of domain borders including P300, RXRA, BCL11A and ELK1.

Chromosomal DNA is tightly packed up in 3D such that around 2 meters of this long molecule fits into the microscopic nucleus of every cell. The genome packing is not random, but instead structured in 3D domains that are essential to numerous key processes in the cell, such as for the regulation of gene expression or for the replication of DNA. A current challenge is to identify the key molecular drivers of this higher-order chromosome organization. Here we propose a novel computational integrative approach to identify proteins and DNA elements that positively or negatively influence the establishment or maintenance of 3D domains. Analysis of Drosophila data at very high resolution suggests that among architectural proteins, BEAF-32 and CP190 are the main positive drivers of 3D domains. In humans, our results highlight the roles of CTCF, cohesin, ZNF143 and Polycomb group proteins as positive drivers of 3D domains, in contrast to P300, RXRA, BCL11A and ELK1 that act as negative drivers.

4D nucleomes in single cells: what can computational modeling reveal about spatial chromatin conformation?

Genome-wide sequencing technologies enable investigations of the structural properties of the genome in various spatial dimensions. Here, we review computational techniques developed to model the three-dimensional genome in single cells versus ensembles of cells and assess their underlying assumptions. We further address approaches to study the spatio-temporal aspects of genome organization from single-cell data.

HSA: integrating multi-track Hi-C data for genome-scale reconstruction of 3D chromatin structure

Genome-wide 3C technologies (Hi-C) are being increasingly employed to study three-dimensional (3D) genome conformations. Existing computational approaches are unable to integrate accumulating data to facilitate studying 3D chromatin structure and function. We present HSA (http://ouyanglab.jax.org/hsa/), a flexible tool that jointly analyzes multiple contact maps to infer 3D chromatin structure at the genome scale. HSA globally searches the latent structure underlying different cleavage footprints. Its robustness and accuracy outperform or rival existing tools on extensive simulations and orthogonal experiment validations. Applying HSA to recent in situ Hi-C data, we found the 3D chromatin structures are highly conserved across various human cell types.

Inferring 3D chromatin structure using a multiscale approach based on quaternions

Background

The knowledge of the spatial organisation of the chromatin fibre in cell nuclei helps researchers to understand the nuclear machinery that regulates dna activity. Recent experimental techniques of the type Chromosome Conformation Capture (3c, or similar) provide high-resolution, high-throughput data consisting in the number of times any possible pair of dna fragments is found to be in contact, in a certain population of cells. As these data carry information on the structure of the chromatin fibre, several attempts have been made to use them to obtain high-resolution 3d reconstructions of entire chromosomes, or even an entire genome. The techniques proposed treat the data in different ways, possibly exploiting physical-geometric chromatin models. One popular strategy is to transform contact data into Euclidean distances between pairs of fragments, and then solve a classical distance-to-geometry problem.

Results

We developed and tested a reconstruction technique that does not require translating contacts into distances, thus avoiding a number of related drawbacks. Also, we introduce a geometrical chromatin chain model that allows us to include sound biochemical and biological constraints in the problem. This model can be scaled at different genomic resolutions, where the structures of the coarser models are influenced by the reconstructions at finer resolutions. The search in the solution space is then performed by a classical simulated annealing, where the model is evolved efficiently through quaternion operators. The presence of appropriate constraints permits the less reliable data to be overlooked, so the result is a set of plausible chromatin configurations compatible with both the data and the prior knowledge.

Conclusions

To test our method, we obtained a number of 3d chromatin configurations from hi-c data available in the literature for the long arm of human chromosome 1, and validated their features against known properties of gene density and transcriptional activity. Our results are compatible with biological features not introduced a priori in the problem: structurally different regions in our reconstructions highly correlate with functionally different regions as known from literature and genomic repositories.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0667-0) contains supplementary material, which is available to authorized users.

On the demultiplexing of chromosome capture conformation data

How to describe the multiple chromosome structures that underlie interactions among genome loci and how to quantify the occurrence of these structures in a cell population remain important challenges to solve, which can be addressed via a proper demultiplexing of chromosome capture conformation related data. Here, we first aim to review two main methodologies that have been proposed to tackle this problem: restrained-based methods, in which the resulting chromosome structures stem from the multiple solutions of a distance satisfaction problem; and thermodynamic-based methods, in which the structures stem from the simulation of polymer models. Next, we propose a novel demultiplexing method based on a matrix decomposition of contact maps. To this end, we extend the notion of topologically associated domains (TADs) by introducing that of statistical interaction domains (SIDs). SIDs can overlap and occur in a cell population at certain frequencies, and we propose a simple method to estimate these frequency values. As an application, we show that SIDs that measure 100kb to tens of Mb long occur both frequently and specifically in the human genome.

Probing long-range interactions by extracting free energies from genome-wide chromosome conformation capture data

Background

A variety of DNA binding proteins are involved in regulating and shaping the packing of chromatin. They aid the formation of loops in the DNA that function to isolate different structural domains. A recent experimental technique, Hi-C, provides a method for determining the frequency of such looping between all distant parts of the genome. Given that the binding locations of many chromatin associated proteins have also been measured, it has been possible to make estimates for their influence on the long-range interactions as measured by Hi-C. However, a challenge in this analysis is the predominance of non-specific contacts that mask out the specific interactions of interest.

Results

We show that transforming the Hi-C contact frequencies into free energies gives a natural method for separating out the distance dependent non-specific interactions. In particular we apply Principal Component Analysis (PCA) to the transformed free energy matrix to identify the dominant modes of interaction. PCA identifies systematic effects as well as high frequency spatial noise in the Hi-C data which can be filtered out. Thus it can be used as a data driven approach for normalizing Hi-C data. We assess this PCA based normalization approach, along with several other normalization schemes, by fitting the transformed Hi-C data using a pairwise interaction model that takes as input the known locations of bound chromatin factors. The result of fitting is a set of predictions for the coupling energies between the various chromatin factors and their effect on the energetics of looping. We show that the quality of the fit can be used as a means to determine how much PCA filtering should be applied to the Hi-C data.

Conclusions

We find that the different normalizations of the Hi-C data vary in the quality of fit to the pairwise interaction model. PCA filtering can improve the fit, and the predicted coupling energies lead to biologically meaningful insights for how various chromatin bound factors influence the stability of DNA loops in chromatin.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0584-2) contains supplementary material, which is available to authorized users.

Restraint-based three-dimensional modeling of genomes and genomic domains

Chromosomes are large polymer molecules composed of nucleotides. In some species, such as humans, this polymer can sum up to meters long and still be properly folded within the nuclear space of few microns in size. The exact mechanisms of how the meters long DNA is folded into the nucleus, as well as how the regulatory machinery can access it, is to a large extend still a mystery. However, and thanks to newly developed molecular, genomic and computational approaches based on the Chromosome Conformation Capture (3C) technology, we are now obtaining insight on how genomes are spatially organized. Here we review a new family of computational approaches that aim at using 3C-based data to obtain spatial restraints for modeling genomes and genomic domains.

Inferential modeling of 3D chromatin structure

For eukaryotic cells, the biological processes involving regulatory DNA elements play an important role in cell cycle. Understanding 3D spatial arrangements of chromosomes and revealing long-range chromatin interactions are critical to decipher these biological processes. In recent years, chromosome conformation capture (3C) related techniques have been developed to measure the interaction frequencies between long-range genome loci, which have provided a great opportunity to decode the 3D organization of the genome. In this paper, we develop a new Bayesian framework to derive the 3D architecture of a chromosome from 3C-based data. By modeling each chromosome as a polymer chain, we define the conformational energy based on our current knowledge on polymer physics and use it as prior information in the Bayesian framework. We also propose an expectation-maximization (EM) based algorithm to estimate the unknown parameters of the Bayesian model and infer an ensemble of chromatin structures based on interaction frequency data. We have validated our Bayesian inference approach through cross-validation and verified the computed chromatin conformations using the geometric constraints derived from fluorescence in situ hybridization (FISH) experiments. We have further confirmed the inferred chromatin structures using the known genetic interactions derived from other studies in the literature. Our test results have indicated that our Bayesian framework can compute an accurate ensemble of 3D chromatin conformations that best interpret the distance constraints derived from 3C-based data and also agree with other sources of geometric constraints derived from experimental evidence in the previous studies. The source code of our approach can be found in https://github.com/wangsy11/InfMod3DGen.

Predictive polymer modeling reveals coupled fluctuations in chromosome conformation and transcription

A new level of chromosome organization, topologically associating domains (TADs), was recently uncovered by chromosome conformation capture (3C) techniques. To explore TAD structure and function, we developed a polymer model that can extract the full repertoire of chromatin conformations within TADs from population-based 3C data. This model predicts actual physical distances and to what extent chromosomal contacts vary between cells. It also identifies interactions within single TADs that stabilize boundaries between TADs and allows us to identify and genetically validate key structural elements within TADs. Combining the model's predictions with high-resolution DNA FISH and quantitative RNA FISH for TADs within the X-inactivation center (Xic), we dissect the relationship between transcription and spatial proximity to cis-regulatory elements. We demonstrate that contacts between potential regulatory elements occur in the context of fluctuating structures rather than stable loops and propose that such fluctuations may contribute to asymmetric expression in the Xic during X inactivation.

The 3DGD: a database of genome 3D structure

The studies of chromatin 3D structure help us to understand its formation and function. Techniques combining chromosome conformation capture and next generation sequencing can capture chromatin structure information and has been applied to several different species and cell lines. We built 3DGD (3D Genome Database), a database that currently collected Hi-C data on four species, for easy accessing and visualization of chromatin 3D structure data. With the integration of other omics data such as genome-wide protein-DNA-binding data, this data source would be useful for researchers interested in chromatin structure and its biological functions.

AVAILABILITY AND IMPLEMENTATION

The 3DGD v1.1, data browser, downloadable files and documentation are available at: http://3dgd.biosino.org/.