Recovering ensembles of chromatin conformations from contact probabilities

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

Efficient Hi-C inversion facilitates chromatin folding mechanism discovery and structure prediction

Genome-wide chromosome conformation capture (Hi-C) experiments have revealed many structural features of chromatin across multiple length scales. Further understanding genome organization requires relating these discoveries to the mechanisms that establish chromatin structures and reconstructing these structures in three dimensions, but both objectives are difficult to achieve with existing algorithms that are often computationally expensive. To alleviate this challenge, we present an algorithm that efficiently converts Hi-C data into contact energies, which measure the interaction strength between genomic loci brought into proximity. Contact energies are local quantities unaffected by the topological constraints that correlate Hi-C contact probabilities. Thus, extracting contact energies from Hi-C contact probabilities distills the biologically unique information contained in the data. We show that contact energies reveal the location of chromatin loop anchors, support a phase separation mechanism for genome compartmentalization, and parameterize polymer simulations that predict three-dimensional chromatin structures. Therefore, we anticipate that contact energy extraction will unleash the full potential of Hi-C data and that our inversion algorithm will facilitate the widespread adoption of contact energy analysis.

Efficient Hi-C inversion facilitates chromatin folding mechanism discovery and structure prediction

Genome-wide chromosome conformation capture (Hi-C) experiments have revealed many structural features of chromatin across multiple length scales. Further understanding genome organization requires relating these discoveries to the mechanisms that establish chromatin structures and reconstructing these structures in three dimensions, but both objectives are difficult to achieve with existing algorithms that are often computationally expensive. To alleviate this challenge, we present an algorithm that efficiently converts Hi-C data into contact energies, which measure the interaction strength between genomic loci brought into proximity. Contact energies are local quantities unaffected by the topological constraints that correlate Hi-C contact probabilities. Thus, extracting contact energies from Hi-C contact probabilities distills the biologically unique information contained in the data. We show that contact energies reveal the location of chromatin loop anchors, support a phase separation mechanism for genome compartmentalization, and parameterize polymer simulations that predict three-dimensional chromatin structures. Therefore, we anticipate that contact energy extraction will unleash the full potential of Hi-C data and that our inversion algorithm will facilitate the widespread adoption of contact energy analysis.

Theory of chromatin organization maintained by active loop extrusion

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

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

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

Analysis of three-dimensional chromatin packing domains by chromatin scanning transmission electron microscopy (ChromSTEM)

Chromatin organization over multiple length scales plays a critical role in the regulation of transcription. Deciphering the interplay of these processes requires high-resolution, three-dimensional, quantitative imaging of chromatin structure in vitro. Herein, we introduce ChromSTEM, a method that utilizes high-angle annular dark-field imaging and tomography in scanning transmission electron microscopy combined with DNA-specific staining for electron microscopy. We utilized ChromSTEM for an in-depth quantification of 3D chromatin conformation with high spatial resolution and contrast, allowing for characterization of higher-order chromatin structure almost down to the level of the DNA base pair. Employing mass scaling analysis on ChromSTEM mass density tomograms, we observed that chromatin forms spatially well-defined higher-order domains, around 80 nm in radius. Within domains, chromatin exhibits a polymeric fractal-like behavior and a radially decreasing mass-density from the center to the periphery. Unlike other nanoimaging and analysis techniques, we demonstrate that our unique combination of this high-resolution imaging technique with polymer physics-based analysis enables us to (i) investigate the chromatin conformation within packing domains and (ii) quantify statistical descriptors of chromatin structure that are relevant to transcription. We observe that packing domains have heterogeneous morphological properties even within the same cell line, underlying the potential role of statistical chromatin packing in regulating gene expression within eukaryotic nuclei.

Uncovering the Principles of Genome Folding by 3D Chromatin Modeling

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

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

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

The 3D Genome Structure of Single Cells

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

Multiscale modeling of genome organization with maximum entropy optimization

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

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

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

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.

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

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

Free energy-based model of CTCF-mediated chromatin looping in the human genome

In recent years, high-throughput techniques have revealed considerable structural organization of the human genome with diverse regions of the chromatin interacting with each other in the form of loops. Some of these loops are quite complex and may encompass regions comprised of many interacting chain segments around a central locus. Popular techniques for extracting this information are chromatin interaction analysis by paired-end tag sequencing (ChIA-PET) and high-throughput chromosome conformation capture (Hi-C). Here, we introduce a physics-based method to predict the three-dimensional structure of chromatin from population-averaged ChIA-PET data. The approach uses experimentally-validated data from human B-lymphoblastoid cells to generate 2D meta-structures of chromatin using a dynamic programming algorithm that explores the chromatin free energy landscape. By generating both optimal and suboptimal meta-structures we can calculate both the free energy and additionally the relative thermodynamic probability. A 3D structure prediction program with applied restraints then can be used to generate the tertiary structures. The main advantage of this approach for population-averaged experimental data is that it provides a way to distinguish between the principal and the spurious contacts. This study also finds that euchromatin appear to have rather precisely regulated 2D meta-structures compared to heterochromatin. The program source-code is available at https://github.com/plewczynski/looper.

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

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

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

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.

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.

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.

How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes

The 3D organization of chromosomes is crucial for regulating gene expression and cell function. Many experimental and polymer modeling efforts are dedicated to deciphering the mechanistic principles behind chromosome folding. Chromosomes are long and densely packed-topologically constrained-polymers. The main challenges are therefore to develop adequate models and simulation methods to investigate properly the multi spatio-temporal scales of such macromolecules. Here, we proposed a generic strategy to develop efficient coarse-grained models for self-avoiding polymers on a lattice. Accounting accurately for the polymer entanglement length and the volumic density, we show that our simulation scheme not only captures the steady-state structural and dynamical properties of the system but also tracks the same dynamics at different coarse-graining. This strategy allows a strong power-law gain in numerical efficiency and offers a systematic way to define reliable coarse-grained null models for chromosomes and to go beyond the current limitations by studying long chromosomes during an extended time period with good statistics. We use our formalism to investigate in details the time evolution of the 3D organization of chromosome 3R (20 Mbp) in drosophila during one cell cycle (20 hours). We show that a combination of our coarse-graining strategy with a one-parameter block copolymer model integrating epigenomic-driven interactions quantitatively reproduce experimental data at the chromosome-scale and predict that chromatin motion is very dynamic during the cell cycle.

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.

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.

Topology of polymer chains under nanoscale confinement

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l_p under a spherical confinement of radius R_c. At low values of l_p/R_c, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l_p/R_c, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l_p/R_c, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

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.

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

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

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.

Dynamic properties of independent chromatin domains measured by correlation spectroscopy in living cells

Background

Genome organization into subchromosomal topologically associating domains (TADs) is linked to cell-type-specific gene expression programs. However, dynamic properties of such domains remain elusive, and it is unclear how domain plasticity modulates genomic accessibility for soluble factors.

Results

Here, we combine and compare a high-resolution topology analysis of interacting chromatin loci with fluorescence correlation spectroscopy measurements of domain dynamics in single living cells. We identify topologically and dynamically independent chromatin domains of ~1 Mb in size that are best described by a loop-cluster polymer model. Hydrodynamic relaxation times and gyration radii of domains are larger for open (161 ± 15 ms, 297 ± 9 nm) than for dense chromatin (88 ± 7 ms, 243 ± 6 nm) and increase globally upon chromatin hyperacetylation or ATP depletion.

Conclusions

Based on the domain structure and dynamics measurements, we propose a loop-cluster model for chromatin domains. It suggests that the regulation of chromatin accessibility for soluble factors displays a significantly stronger dependence on factor concentration than search processes within a static network.

Electronic supplementary material

The online version of this article (doi:10.1186/s13072-016-0093-1) contains supplementary material, which is available to authorized users.

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.

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

Combining genome-wide structural models with phenomenological data is at the forefront of efforts to understand the organizational principles regulating the human genome. Here, we use chromosome-chromosome contact data as knowledge-based constraints for large-scale three-dimensional models of the human diploid genome. The resulting models remain minimally entangled and acquire several functional features that are observed in vivo and that were never used as input for the model. We find, for instance, that gene-rich, active regions are drawn towards the nuclear center, while gene poor and lamina associated domains are pushed to the periphery. These and other properties persist upon adding local contact constraints, suggesting their compatibility with non-local constraints for the genome organization. The results show that suitable combinations of data analysis and physical modelling can expose the unexpectedly rich functionally-related properties implicit in chromosome-chromosome contact data. Specific directions are suggested for further developments based on combining experimental data analysis and genomic structural modelling.

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

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

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

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

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.

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.

Dynamics of nanoparticle assembly from disjointed images of nanoparticle-polymer composites

Understanding how nanoparticles (NPs) diffuse, stick, and assemble into larger structures within polymers is key to the design and fabrication of NP-polymer composites. Here we describe an approach for inferring the dynamic parameters of NP assembly from spatially and temporally disjointed images of composites. The approach involves iterative adjustment of the parameters of a kinetic model of assembly until the computed size statistics of NP clusters match those obtained from high-throughput analysis of the experimental images. Application of this approach to the assembly of shaped, metal NPs in polymer films suggests that NP structures grow via a cluster-cluster aggregation mechanism, where NPs and their clusters diffuse with approximately Stokes-Einstein diffusivity and stick to other NPs or clusters with a probability that depends strongly on the size and shape of the NPs and the molecular weight of the polymer.

Integrative meta-analysis of multiple gene expression profiles in acquired gemcitabine-resistant cancer cell lines to identify novel therapeutic biomarkers

In molecular-targeted cancer therapy, acquired resistance to gemcitabine is a major clinical problem that reduces its effectiveness, resulting in recurrence and metastasis of cancers. In spite of great efforts to reveal the overall mechanism of acquired gemcitabine resistance, no definitive genetic factors have been identified that are absolutely responsible for the resistance process. Therefore, we performed a cross-platform meta-analysis of three publically available microarray datasets for cancer cell lines with acquired gemcitabine resistance, using the R-based RankProd algorithm, and were able to identify a total of 158 differentially expressed genes (DEGs; 76 up- and 82 down-regulated) that are potentially involved in acquired resistance to gemcitabine. Indeed, the top 20 up- and down-regulated DEGs are largely associated with a common process of carcinogenesis in many cells. For the top 50 up- and down-regulated DEGs, we conducted integrated analyses of a gene regulatory network, a gene co-expression network, and a protein-protein interaction network. The identified DEGs were functionally enriched via Gene Ontology hierarchy and Kyoto Encyclopedia of Genes and Genomes pathway analyses. By systemic combinational analysis of the three molecular networks, we could condense the total number of DEGs to final seven genes. Notably, GJA1, LEF1, and CCND2 were contained within the lists of the top 20 up- or down-regulated DEGs. Our study represents a comprehensive overview of the gene expression patterns associated with acquired gemcitabine resistance and theoretical support for further clinical therapeutic studies.

Quantification of DNA cleavage specificity in Hi-C experiments

Hi-C experiments produce large numbers of DNA sequence read pairs that are typically analyzed to deduce genomewide interactions between arbitrary loci. A key step in these experiments is the cleavage of cross-linked chromatin with a restriction endonuclease. Although this cleavage should happen specifically at the enzyme's recognition sequence, an unknown proportion of cleavage events may involve other sequences, owing to the enzyme's star activity or to random DNA breakage. A quantitative estimation of these non-specific cleavages may enable simulating realistic Hi-C read pairs for validation of downstream analyses, monitoring the reproducibility of experimental conditions and investigating biophysical properties that correlate with DNA cleavage patterns. Here we describe a computational method for analyzing Hi-C read pairs to estimate the fractions of cleavages at different possible targets. The method relies on expressing an observed local target distribution downstream of aligned reads as a linear combination of known conditional local target distributions. We validated this method using Hi-C read pairs obtained by computer simulation. Application of the method to experimental Hi-C datasets from murine cells revealed interesting similarities and differences in patterns of cleavage across the various experiments considered.

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.

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.

Efficient estimation of contact probabilities from inter-bead distance distributions in simulated polymer chains

The estimation of contact probabilities (CP) from conformations of simulated bead-chain polymer models is a key step in methods that aim to elucidate the spatial organization of chromatin from analysis of experimentally determined contacts between different genomic loci. Although CPs can be estimated simply by counting contacts between beads in a sample of simulated chain conformations, reliable estimation of small CPs through this approach requires a large number of conformations, which can be computationally expensive to obtain. Here we describe an alternative computational method for estimating relatively small CPs without requiring large samples of chain conformations. In particular, we estimate the CPs from functional approximations to the cumulative distribution function (cdf) of the inter-bead distance for each pair of beads. These cdf approximations are obtained by fitting the extended generalized lambda distribution (EGLD) to inter-bead distances determined from a sample of chain conformations, which are in turn generated by Monte Carlo simulations. We find that CPs estimated from fitted EGLD cdfs are significantly more accurate than CPs estimated using contact counts from samples of limited size, and are more precise with all sample sizes, permitting as much as a tenfold reduction in conformation sample size for chains of 200 beads and samples smaller than 10(5) conformations. This method of CP estimation thus has potential to accelerate computational efforts to elucidate the spatial organization of chromatin.

Cell-imprinted substrates act as an artificial niche for skin regeneration

Bioinspired materials can mimic the stem cell environment and modulate stem cell differentiation and proliferation. In this study, biomimetic micro/nanoenvironments were fabricated by cell-imprinted substrates based on mature human keratinocyte morphological templates. The data obtained from atomic force microscopy and field emission scanning electron microscopy revealed that the keratinocyte-cell-imprinted poly(dimethylsiloxane) casting procedure could imitate the surface morphology of the plasma membrane, ranging from the nanoscale to the macroscale, which may provide the required topographical cell fingerprints to induce differentiation. Gene expression levels of the genes analyzed (involucrin, collagen type I, and keratin 10) together with protein expression data showed that human adipose-derived stem cells (ADSCs) seeded on these cell-imprinted substrates were driven to adopt the specific shape and characteristics of keratinocytes. The observed morphology of the ADSCs grown on the keratinocyte casts was noticeably different from that of stem cells cultivated on the stem-cell-imprinted substrates. Since the shape and geometry of the nucleus could potentially alter the gene expression, we used molecular dynamics to probe the effect of the confining geometry on the chain arrangement of simulated chromatin fibers in the nuclei. The results obtained suggested that induction of mature cell shapes onto stem cells can influence nucleus deformation of the stem cells followed by regulation of target genes. This might pave the way for a reliable, efficient, and cheap approach of controlling stem cell differentiation toward skin cells for wound healing applications.

Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains

Genomes of eukaryotes are partitioned into domains of functionally distinct chromatin states. These domains are stably inherited across many cell generations and can be remodeled in response to developmental and external cues, hence contributing to the robustness and plasticity of expression patterns and cell phenotypes. Remarkably, recent studies indicate that these 1D epigenomic domains tend to fold into 3D topologically associated domains forming specialized nuclear chromatin compartments. However, the general mechanisms behind such compartmentalization including the contribution of epigenetic regulation remain unclear. Here, we address the question of the coupling between chromatin folding and epigenome. Using polymer physics, we analyze the properties of a block copolymer model that accounts for local epigenomic information. Considering copolymers build from the epigenomic landscape of Drosophila, we observe a very good agreement with the folding patterns observed in chromosome conformation capture experiments. Moreover, this model provides a physical basis for the existence of multistability in epigenome folding at sub-chromosomal scale. We show how experiments are fully consistent with multistable conformations where topologically associated domains of the same epigenomic state interact dynamically with each other. Our approach provides a general framework to improve our understanding of chromatin folding during cell cycle and differentiation and its relation to epigenetics.

The sequencing bias relaxed characteristics of Hi-C derived data and implications for chromatin 3D modeling

The 3D chromatin structure modeling by chromatin interactions derived from Hi-C experiments is significantly challenged by the intrinsic sequencing biases in these experiments. Conventional modeling methods only focus on the bias among different chromatin regions within the same experiment but neglect the bias arising from different experimental sequencing depth. We now show that the regional interaction bias is tightly coupled with the sequencing depth, and we further identify a chromatin structure parameter as the inherent characteristics of Hi-C derived data for chromatin regions. Then we present an approach for chromatin structure prediction capable of relaxing both kinds of sequencing biases by using this identified parameter. This method is validated by intra and inter cell-line comparisons among various chromatin regions for four human cell-lines (K562, GM12878, IMR90 and H1hESC), which shows that the openness of chromatin region is well correlated with chromatin function. This method has been executed by an automatic pipeline (AutoChrom3D) and thus can be conveniently used.