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

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.

Modeling and simulation of cell nuclear architecture reorganization process

We develop a special phase field/diffusive interface method to model the nuclear architecture reorganization process. In particular, we use a Lagrange multiplier approach in the phase field model to preserve the specific physical and geometrical constraints for the biological events. We develop several efficient and robust linear and weakly nonlinear schemes for this new model. To validate the model and numerical methods, we present ample numerical simulations which in particular reproduce several processes of nuclear architecture reorganization from the experiment literature.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Extracting multi-way chromatin contacts from Hi-C data

There is a growing realization that multi-way chromatin contacts formed in chromosome structures are fundamental units of gene regulation. However, due to the paucity and complexity of such contacts, it is challenging to detect and identify them using experiments. Based on an assumption that chromosome structures can be mapped onto a network of Gaussian polymer, here we derive analytic expressions for n-body contact probabilities (n > 2) among chromatin loci based on pairwise genomic contact frequencies available in Hi-C, and show that multi-way contact probability maps can in principle be extracted from Hi-C. The three-body (triplet) contact probabilities, calculated from our theory, are in good correlation with those from measurements including Tri-C, MC-4C and SPRITE. Maps of multi-way chromatin contacts calculated from our analytic expressions can not only complement experimental measurements, but also can offer better understanding of the related issues, such as cell-line dependent assemblies of multiple genes and enhancers to chromatin hubs, competition between long-range and short-range multi-way contacts, and condensates of multiple CTCF anchors.

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

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

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.

Orc4 spatiotemporally stabilizes centromeric chromatin

The establishment of centromeric chromatin and its propagation by the centromere-specific histone CENPA is mediated by epigenetic mechanisms in most eukaryotes. DNA replication origins, origin binding proteins, and replication timing of centromere DNA are important determinants of centromere function. The epigenetically regulated regional centromeres in the budding yeast Candida albicans have unique DNA sequences that replicate earliest in every chromosome and are clustered throughout the cell cycle. In this study, the genome-wide occupancy of the replication initiation protein Orc4 reveals its abundance at all centromeres in C. albicans Orc4 is associated with four different DNA sequence motifs, one of which coincides with tRNA genes (tDNA) that replicate early and cluster together in space. Hi-C combined with genome-wide replication timing analyses identify that early replicating Orc4-bound regions interact with themselves stronger than with late replicating Orc4-bound regions. We simulate a polymer model of chromosomes of C. albicans and propose that the early replicating and highly enriched Orc4-bound sites preferentially localize around the clustered kinetochores. We also observe that Orc4 is constitutively localized to centromeres, and both Orc4 and the helicase Mcm2 are essential for cell viability and CENPA stability in C. albicans Finally, we show that new molecules of CENPA are recruited to centromeres during late anaphase/telophase, which coincides with the stage at which the CENPA-specific chaperone Scm3 localizes to the kinetochore. We propose that the spatiotemporal localization of Orc4 within the nucleus, in collaboration with Mcm2 and Scm3, maintains centromeric chromatin stability and CENPA recruitment in C. albicans.

Exploring chromosomal structural heterogeneity across multiple cell lines

Using computer simulations, we generate cell-specific 3D chromosomal structures and compare them to recently published chromatin structures obtained through microscopy. We demonstrate using machine learning and polymer physics simulations that epigenetic information can be used to predict the structural ensembles of multiple human cell lines. Theory predicts that chromosome structures are fluid and can only be described by an ensemble, which is consistent with the observation that chromosomes exhibit no unique fold. Nevertheless, our analysis of both structures from simulation and microscopy reveals that short segments of chromatin make two-state transitions between closed conformations and open dumbbell conformations. Finally, we study the conformational changes associated with the switching of genomic compartments observed in human cell lines. The formation of genomic compartments resembles hydrophobic collapse in protein folding, with the aggregation of denser and predominantly inactive chromatin driving the positioning of active chromatin toward the surface of individual chromosomal territories.

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

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

CHROMATIX: computing the functional landscape of many-body chromatin interactions in transcriptionally active loci from deconvolved single cells

Chromatin interactions are important for gene regulation and cellular specialization. Emerging evidence suggests many-body spatial interactions play important roles in condensing super-enhancer regions into a cohesive transcriptional apparatus. Chromosome conformation studies using Hi-C are limited to pairwise, population-averaged interactions; therefore unsuitable for direct assessment of many-body interactions. We describe a computational model, CHROMATIX, which reconstructs ensembles of single-cell chromatin structures by deconvolving Hi-C data and identifies significant many-body interactions. For a diverse set of highly active transcriptional loci with at least 2 super-enhancers, we detail the many-body functional landscape and show DNase accessibility, POLR2A binding, and decreased H3K27me3 are predictive of interaction-enriched regions.

The 4D Nucleome: Genome Compartmentalization in an Evolutionary Context

4D nucleome research aims to understand the impact of nuclear organization in space and time on nuclear functions, such as gene expression patterns, chromatin replication, and the maintenance of genome integrity. In this review we describe evidence that the origin of 4D genome compartmentalization can be traced back to the prokaryotic world. In cell nuclei of animals and plants chromosomes occupy distinct territories, built up from ~1 Mb chromatin domains, which in turn are composed of smaller chromatin subdomains and also form larger chromatin domain clusters. Microscopic evidence for this higher order chromatin landscape was strengthened by chromosome conformation capture studies, in particular Hi-C. This approach demonstrated ~1 Mb sized, topologically associating domains in mammalian cell nuclei separated by boundaries. Mutations, which destroy boundaries, can result in developmental disorders and cancer. Nucleosomes appeared first as tetramers in the Archaea kingdom and later evolved to octamers built up each from two H2A, two H2B, two H3, and two H4 proteins. Notably, nucleosomes were lost during the evolution of the Dinoflagellata phylum. Dinoflagellate chromosomes remain condensed during the entire cell cycle, but their chromosome architecture differs radically from the architecture of other eukaryotes. In summary, the conservation of fundamental features of higher order chromatin arrangements throughout the evolution of metazoan animals suggests the existence of conserved, but still unknown mechanism(s) controlling this architecture. Notwithstanding this conservation, a comparison of metazoans and protists also demonstrates species-specific structural and functional features of nuclear organization.

Super-resolution Imaging of Individual Human Subchromosomal Regions in Situ Reveals Nanoscopic Building Blocks of Higher-Order Structure

It is widely recognized that the higher-order spatial organization of the genome, beyond the nucleosome, plays an important role in many biological processes. However, to date, direct information on even such fundamental structural details as the typical sizes and DNA content of these higher-order structures in situ is poorly characterized. Here, we examine the nanoscopic DNA organization within human nuclei using super-resolution direct stochastic optical reconstruction microscopy (dSTORM) imaging and 5-ethynyl-2'-deoxyuridine click chemistry, studying single fully labeled chromosomes within an otherwise unlabeled nuclei to improve the attainable resolution. We find that, regardless of nuclear position, individual subchromosomal regions consist of three different levels of DNA compaction: (i) dispersed chromatin; (ii) nanodomains of sizes ranging tens of nanometers containing a few kilobases (kb) of DNA; and (iii) clusters of nanodomains. Interestingly, the sizes and DNA content of the nanodomains are approximately the same at the nuclear periphery, nucleolar proximity, and nuclear interior, suggesting that these nanodomains share a roughly common higher-order architecture. Overall, these results suggest that DNA compaction within the eukaryote nucleus occurs via the condensation of DNA into few-kb nanodomains of approximately similar structure, with further compaction occurring via the clustering of nanodomains.

De novo prediction of human chromosome structures: Epigenetic marking patterns encode genome architecture

Inside the cell nucleus, genomes fold into organized structures that are characteristic of cell type. Here, we show that this chromatin architecture can be predicted de novo using epigenetic data derived from chromatin immunoprecipitation-sequencing (ChIP-Seq). We exploit the idea that chromosomes encode a 1D sequence of chromatin structural types. Interactions between these chromatin types determine the 3D structural ensemble of chromosomes through a process similar to phase separation. First, a neural network is used to infer the relation between the epigenetic marks present at a locus, as assayed by ChIP-Seq, and the genomic compartment in which those loci reside, as measured by DNA-DNA proximity ligation (Hi-C). Next, types inferred from this neural network are used as an input to an energy landscape model for chromatin organization [Minimal Chromatin Model (MiChroM)] to generate an ensemble of 3D chromosome conformations at a resolution of 50 kilobases (kb). After training the model, dubbed Maximum Entropy Genomic Annotation from Biomarkers Associated to Structural Ensembles (MEGABASE), on odd-numbered chromosomes, we predict the sequences of chromatin types and the subsequent 3D conformational ensembles for the even chromosomes. We validate these structural ensembles by using ChIP-Seq tracks alone to predict Hi-C maps, as well as distances measured using 3D fluorescence in situ hybridization (FISH) experiments. Both sets of experiments support the hypothesis of phase separation being the driving process behind compartmentalization. These findings strongly suggest that epigenetic marking patterns encode sufficient information to determine the global architecture of chromosomes and that de novo structure prediction for whole genomes may be increasingly possible.

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

[This corrects the article DOI: 10.1371/journal.pcbi.1005658.].