Uncovering the statistical physics of 3D chromosomal organization using data-driven modeling

In recent years, much effort has been devoted to understanding the three-dimensional (3D) organization of the genome and how genomic structure mediates nuclear function. The development of experimental techniques that combine DNA proximity ligation with high-throughput sequencing, such as Hi-C, have substantially improved our knowledge about chromatin organization. Numerous experimental advancements, not only utilizing DNA proximity ligation but also high-resolution genome imaging (DNA tracing), have required theoretical modeling to determine the structural ensembles consistent with such data. These 3D polymer models of the genome provide an understanding of the physical mechanisms governing genome architecture. Here, we present an overview of the recent advances in modeling the ensemble of 3D chromosomal structures by employing the maximum entropy approach combined with polymer physics. Particularly, we discuss the minimal chromatin model (MiChroM) along with the “maximum entropy genomic annotations from biomarkers associated with structural ensembles” (MEGABASE) model, which have been remarkably successful in the accurate modeling of chromosomes consistent with both Hi-C and DNA-tracing data.     

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.     

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

The one-dimensional information of genomic DNA is hierarchically packed inside the eukaryotic cell nucleus and organized in a three-dimensional (3D) space. Genome-wide chromosome conformation capture (Hi-C) methods have uncovered the 3D genome organization and revealed multiscale chromatin domains of compartments and topologically associating domains (TADs). Moreover, single-nucleosome live-cell imaging experiments have revealed the dynamic organization of chromatin domains caused by stochastic thermal fluctuations. However, the mechanism underlying the dynamic regulation of such hierarchical and structural chromatin units within the microscale thermal medium remains unclear. Microrheology is a way to measure dynamic viscoelastic properties coupling between thermal microenvironment and mechanical response. Here, we propose a new, to our knowledge, microrheology for Hi-C data to analyze the dynamic compliance property as a measure of rigidness and flexibility of genomic regions along with the time evolution. Our method allows the conversion of an Hi-C matrix into the spectrum of the dynamic rheological property along the genomic coordinate of a single chromosome. To demonstrate the power of the technique, we analyzed Hi-C data during the neural differentiation of mouse embryonic stem cells. We found that TAD boundaries behave as more rigid nodes than the intra-TAD regions. The spectrum clearly shows the dynamic viscoelasticity of chromatin domain formation at different timescales. Furthermore, we characterized the appearance of synchronous and liquid-like intercompartment interactions in differentiated cells. Together, our microrheology data derived from Hi-C data provide physical insights into the dynamics of the 3D genome organization.     

Advances in higher-order chromatin architecture: the move towards 4D genome

In eukaryotes, the genome is hierarchically packed inside the nucleus, which facilitates physical contact between cis-regulatory elements (CREs), such as enhancers and promoters. Accumulating evidence highlights the critical role of higher-order chromatin structure in precise regulation of spatiotemporal gene expression under diverse biological contexts including lineage commitment and cell activation by external stimulus. Genomics and imaging-based technologies, such as Hi-C and DNA fluorescence in situ hybridization (FISH), have revealed the key principles of genome folding, while newly developed tools focus on improvement in resolution, throughput and modality at single-cell and population levels, and challenge the knowledge obtained through conventional approaches. In this review, we discuss recent advances in our understanding of principles of higher-order chromosome conformation and technologies to investigate 4D chromatin interactions.     

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.     

ASHIC: hierarchical Bayesian modeling of diploid chromatin contacts and structures

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

Segmentation of Image Data from Complex Organotypic 3D Models of Cancer Tissues with Markov Random Fields

Organotypic, three dimensional (3D) cell culture models of epithelial tumour types such as prostate cancer recapitulate key aspects of the architecture and histology of solid cancers. Morphometric analysis of multicellular 3D organoids is particularly important when additional components such as the extracellular matrix and tumour microenvironment are included in the model. The complexity of such models has so far limited their successful implementation. There is a great need for automatic, accurate and robust image segmentation tools to facilitate the analysis of such biologically relevant 3D cell culture models. We present a segmentation method based on Markov random fields (MRFs) and illustrate our method using 3D stack image data from an organotypic 3D model of prostate cancer cells co-cultured with cancer-associated fibroblasts (CAFs). The 3D segmentation output suggests that these cell types are in physical contact with each other within the model, which has important implications for tumour biology. Segmentation performance is quantified using ground truth labels and we show how each step of our method increases segmentation accuracy. We provide the ground truth labels along with the image data and code. Using independent image data we show that our segmentation method is also more generally applicable to other types of cellular microscopy and not only limited to fluorescence microscopy.     

Recovering ensembles of chromatin conformations from contact probabilities

The 3D higher order organization of chromatin within the nucleus of eukaryotic cells has so far remained elusive. A wealth of relevant information, however, is increasingly becoming available from chromosome conformation capture (3C) and related experimental techniques, which measure the probabilities of contact between large numbers of genomic sites in fixed cells. Such contact probabilities (CPs) can in principle be used to deduce the 3D spatial organization of chromatin. Here, we propose a computational method to recover an ensemble of chromatin conformations consistent with a set of given CPs. Compared with existing alternatives, this method does not require conversion of CPs to mean spatial distances. Instead, we estimate CPs by simulating a physically realistic, bead-chain polymer model of the 30-nm chromatin fiber. We then use an approach from adaptive filter theory to iteratively adjust the parameters of this polymer model until the estimated CPs match the given CPs. We have validated this method against reference data sets obtained from simulations of test systems with up to 45 beads and 4 loops. With additional testing against experiments and with further algorithmic refinements, our approach could become a valuable tool for researchers examining the higher order organization of chromatin.     

Developing bioimaging and quantitative methods to study 3D genome

The recent advances in chromosome configuration capture (3C)-based series molecular methods and optical super-resolution (SR) techniques offer powerful tools to investigate three dimensional (3D) genomic structure in prokaryotic and eukaryotic cell nucleus. In this review, we focus on the progress during the last decade in this exciting field. Here we at first introduce briefly genome organization at chromosome, domain and sub-domain level, respectively; then we provide a short introduction to various super-resolution microscopy techniques which can be employed to detect genome 3D structure. We also reviewed the progress of quantitative and visualization tools to evaluate and visualize chromatin interactions in 3D genome derived from Hi-C data. We end up with the discussion that imaging methods and 3C-based molecular methods are not mutually exclusive - - - - actually they are complemental to each other and can be combined together to study 3D genome organization.     

Large-scale reconstruction of 3D structures of human chromosomes from chromosomal contact data

Chromosomes are not positioned randomly within a nucleus, but instead, they adopt preferred spatial conformations to facilitate necessary long-range gene–gene interactions and regulations. Thus, obtaining the 3D shape of chromosomes of a genome is critical for understanding how the genome folds, functions and how its genes interact and are regulated. Here, we describe a method to reconstruct preferred 3D structures of individual chromosomes of the human genome from chromosomal contact data generated by the Hi-C chromosome conformation capturing technique. A novel parameterized objective function was designed for modeling chromosome structures, which was optimized by a gradient descent method to generate chromosomal structural models that could satisfy as many intra-chromosomal contacts as possible. We applied the objective function and the corresponding optimization method to two Hi-C chromosomal data sets of both a healthy and a cancerous human B-cell to construct 3D models of individual chromosomes at resolutions of 1 MB and 200 KB, respectively. The parameters used with the method were calibrated according to an independent fluorescence in situ hybridization experimental data. The structural models generated by our method could satisfy a high percentage of contacts (pairs of loci in interaction) and non-contacts (pairs of loci not in interaction) and were compatible with the known two-compartment organization of human chromatin structures. Furthermore, structural models generated at different resolutions and from randomly permuted data sets were consistent.     

三维基因组学与精准生物学

三维基因组学是以研究真核生物核内基因组空间构象,及其对不同基因转录调控的生物学效应为主要研究内容的一个新的学科方向;也是后基因组学时代研究的一个热门领域。它的研究重点是空间构象与基因转录调控间的关系。通过三维基因组学技术,科学家将能对基因组的折叠和空间构象、转录调控机制、复杂生物学性状、信号传导通路和基因组的运行机制等一系列重要问题进行更深入的探讨和研究,为系统解读生命百科全书和精准生物学的实施奠定坚实基础。本文综述了目前三维基因组学研究领域中的主要技术、研究现状、科研进展、存在问题、未来及与精准生物学的关系等内容。以期能较系统地展示三维基因组学取得的一系列成果,解读从三维空间构象信息到不同基因功能研究的路径,精准决定在转录调控网络中不同基因表达的时空特异性的可能模式。     

Tracking and interpreting long-range chromatin interactions with super-resolution live-cell imaging

Mammalian genomes are organized and regulated through long-range chromatin interactions. Structural loops formed by CCCTC-binding factor (CTCF) and cohesin fold the genome into domains, while enhancers interact with promoters across vast genomic distances to regulate gene expression. Although genomics and fixed-cell imaging approaches help illuminate many aspects of chromatin interactions, temporal information is usually lost. Here, we discuss how 3D super-resolution live-cell imaging (SRLCI) can resolve open questions on the dynamic formation and dissolution of chromatin interactions. We discuss SRLCI experimental design, implementation strategies, and data interpretation and highlight associated pitfalls. We conclude that, while technically demanding, SRLCI approaches will likely emerge as a critical tool to dynamically probe 3D genome structure and function and to study enhancer–promoter interactions and chromatin looping.     

Advances in technologies for 3D genomics research

The spatial structure of the orderly organized chromatin in the nucleus has important roles in maintaining normal cell function and in regulation of gene expression, and the high-throughput Hi-C and Ch IA-PET methods have been widely used in various biological studies for determining potential spatial genome structures and their functions. However, there are still great difficulties and challenges in three-dimensional(3D) genomics research. More efficient, economical, and unbiased approaches to studying 3D genomics need to be developed for more widespread and easier applications. Here, we review the most recent studies on new 3D genomics research technologies, such as improvements of the traditional Hi-C and Ch IA-PET methods, new approaches based on non-proximal-ligation strategies, and imaging-based methods improved in recent years. Especially, we review the CRISPR-based methods for functional validations in 3D genomics, which could be the forthcoming directions. We hope this review can show some insights into the potential improvements for future 3D genomics.     

Higher-order chromatin structure: bridging physics and biology

Advances in microscopy and genomic techniques have provided new insight into spatial chromatin organization inside of the nucleus. In particular, chromosome conformation capture data has highlighted the relevance of polymer physics for high-order chromatin organization. In this context, we review basic polymer states, discuss how an appropriate polymer model can be determined from experimental data, and examine the success and limitations of various polymer models of higher-order interphase chromatin organization. By taking into account topological constraints acting on the chromatin fiber, recently developed polymer models of interphase chromatin can reproduce the observed scaling of distances between genomic loci, chromosomal territories, and probabilities of contacts between loci measured by chromosome conformation capture methods. Polymer models provide a framework for the interpretation of experimental data as ensembles of conformations rather than collections of loops, and will be crucial for untangling functional implications of chromosomal organization.