A predictive computational model of the dynamic 3D interphase yeast nucleus

Computational methods for analysing multiscale 3D genome organization

Recent progress in whole-genome mapping and imaging technologies has enabled the characterization of the spatial organization and folding of the genome in the nucleus. In parallel, advanced computational methods have been developed to leverage these mapping data to reveal multiscale three-dimensional (3D) genome features and to provide a more complete view of genome structure and its connections to genome functions such as transcription. Here, we discuss how recently developed computational tools, including machine-learning-based methods and integrative structure-modelling frameworks, have led to a systematic, multiscale delineation of the connections among different scales of 3D genome organization, genomic and epigenomic features, functional nuclear components and genome function. However, approaches that more comprehensively integrate a wide variety of genomic and imaging datasets are still needed to uncover the functional role of 3D genome structure in defining cellular phenotypes in health and disease.

The power of weak, transient interactions across biology: A paradigm of emergent behavior

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Structure and dynamics of chemically active ring polymers: swelling to collapse

The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.

Evaluating the role of the nuclear microenvironment in gene function by population-based modeling

The nuclear folding of chromosomes relative to nuclear bodies is an integral part of gene function. Here, we demonstrate that population-based modeling-from ensemble Hi-C data-provides a detailed description of the nuclear microenvironment of genes and its role in gene function. We define the microenvironment by the subnuclear positions of genomic regions with respect to nuclear bodies, local chromatin compaction, and preferences in chromatin compartmentalization. These structural descriptors are determined in single-cell models, thereby revealing the structural variability between cells. We demonstrate that the microenvironment of a genomic region is linked to its functional potential in gene transcription, replication, and chromatin compartmentalization. Some chromatin regions feature a strong preference for a single microenvironment, due to association with specific nuclear bodies in most cells. Other chromatin shows high structural variability, which is a strong indicator of functional heterogeneity. Moreover, we identify specialized nuclear microenvironments, which distinguish chromatin in different functional states and reveal a key role of nuclear speckles in chromosome organization. We demonstrate that our method produces highly predictive three-dimensional genome structures, which accurately reproduce data from a variety of orthogonal experiments, thus considerably expanding the range of Hi-C data analysis.

Ultrastructure and fractal property of chromosomes in close-to-native yeast nuclei visualized using X-ray laser diffraction

Genome compaction and activity in the nucleus depend on spatiotemporal changes in the organization of chromatins in chromosomes. However, the direct imaging of the chromosome structures in the nuclei has been difficult and challenging. Herein, we directly visualized the structure of chromosomes in frozen-hydrated nuclei of budding yeast in the interphase using X-ray laser diffraction. The reconstructed projection electron density maps revealed inhomogeneous distributions of chromosomes, such as a 300 nm assembly and fibrous substructures in the elliptic-circular shaped nuclei of approximately 800 nm. In addition, from the diffraction patterns, we confirmed the absence of regular arrangements of chromosomes and chromatins with 400-20 nm spacing, and demonstrated that chromosomes were composed of self-similarly assembled substructural domains with an average radius of gyration of 58 nm and smooth surfaces. Based on these analyses, we constructed putative models to discuss the organization of 16 chromosomes, carrying DNA of 4.1 mm in 800 nm ellipsoid of the nucleus at the interphase. We anticipate the structural parameters on the fractal property of chromosomes and the experimental images to be a starting point for constructing more sophisticated 3D structural models of the nucleus.

Strong interactions between highly dynamic lamina-associated domains and the nuclear envelope stabilize the 3D architecture of Drosophila interphase chromatin

BACKGROUND

Interactions among topologically associating domains (TADs), and between the nuclear envelope (NE) and lamina-associated domains (LADs) are expected to shape various aspects of three-dimensional (3D) chromatin structure and dynamics; however, relevant genome-wide experiments that may provide statistically significant conclusions remain difficult.

RESULTS

We have developed a coarse-grained dynamical model of D. melanogaster nuclei at TAD resolution that explicitly accounts for four distinct epigenetic classes of TADs and LAD-NE interactions. The model is parameterized to reproduce the experimental Hi-C map of the wild type (WT) nuclei; it describes time evolution of the chromatin over the G1 phase of the interphase. The simulations include an ensemble of nuclei, corresponding to the experimentally observed set of several possible mutual arrangements of chromosomal arms. The model is validated against multiple structural features of chromatin from several different experiments not used in model development. Predicted positioning of all LADs at the NE is highly dynamic-the same LAD can attach, detach and move far away from the NE multiple times during interphase. The probabilities of LADs to be in contact with the NE vary by an order of magnitude, despite all having the same affinity to the NE in the model. These probabilities are mostly determined by a highly variable local linear density of LADs along the genome, which also has the same strong effect on the predicted positioning of individual TADs -- higher probability of a TAD to be near NE is largely determined by a higher linear density of LADs surrounding this TAD. The distribution of LADs along the chromosome chains plays a notable role in maintaining a non-random average global structure of chromatin. Relatively high affinity of LADs to the NE in the WT nuclei substantially reduces sensitivity of the global radial chromatin distribution to variations in the strength of TAD-TAD interactions compared to the lamin depleted nuclei, where a small (0.5 kT) increase of cross-type TAD-TAD interactions doubles the chromatin density in the central nucleus region.

CONCLUSIONS

A dynamical model of the entire fruit fly genome makes multiple genome-wide predictions of biological interest. The distribution of LADs along the chromatin chains affects their probabilities to be in contact with the NE and radial positioning of highly mobile TADs, playing a notable role in creating a non-random average global structure of the chromatin. We conjecture that an important role of attractive LAD-NE interactions is to stabilize global chromatin structure against inevitable cell-to-cell variations in TAD-TAD interactions.

Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing.

Karyotype engineering reveals spatio-temporal control of replication firing and gene contacts

Eukaryotic genomes vary in terms of size, chromosome number, and genetic complexity. Their temporal organization is complex, reflecting coordination between DNA folding and function. Here, we used fused karyotypes of budding yeast to characterize the effects of chromosome length on nuclear architecture. We found that size-matched megachromosomes expand to occupy a larger fraction of the enlarged nucleus. Hi-C maps reveal changes in the three-dimensional structure corresponding to inactivated centromeres and telomeres. De-clustering of inactive centromeres results in their loss of early replication, highlighting a functional correlation between genome organization and replication timing. Repositioning of former telomere-proximal regions on chromosome arms exposed a subset of contacts between flocculin genes. Chromatin reorganization of megachromosomes during cell division remained unperturbed, and it revealed that centromere-rDNA contacts in anaphase, extending over 0.3 Mb on wild-type chromosome, cannot exceed ∼1.7 Mb. Our results highlight the relevance of engineered karyotypes to unveiling relationships between genome organization and function.

Mathematical model of chromosomal dynamics during DNA double strand break repair in budding yeast

During the repair of double-strand breaks (DSBs) in DNA, active mobilizations for conformational changes in chromosomes have been widely observed in eukaryotes, from yeast to animal and plant cells. DSB-damaged loci in the yeast genome showed increased mobility and relocation to the nuclear periphery. However, the driving forces behind DSB-induced chromatin dynamics remain unclear. In this study, mathematical models of normal and DSB-damaged yeast chromosomes were developed to simulate their structural dynamics. The effects of histone degradation in the whole nucleus and the change in the physical properties of damaged loci due to the binding of SUMOylated repair proteins were considered in the model of DSB-induced chromosomes based on recent experimental results. The simulation results reproduced DSB-induced changes to structural and dynamical features by which the combination of whole nuclear histone degradation and the rigid structure formation of repair protein accumulations on damaged loci were suggested to be primary contributors to the process by which damaged loci are relocated to the nuclear periphery.

Chemically Induced Chromosomal Interaction (CICI) method to study chromosome dynamics and its biological roles

Numerous intra- and inter-chromosomal contacts have been mapped in eukaryotic genomes, but it remains challenging to link these 3D structures to their regulatory functions. To establish the causal relationships between chromosome conformation and genome functions, we  develop a method, Chemically Induced Chromosomal Interaction (CICI), to selectively perturb the chromosome conformation at targeted loci. Using this method, long-distance chromosomal interactions can be induced dynamically between intra- or inter-chromosomal loci pairs, including the ones with very low Hi-C contact frequencies. Measurement of CICI formation time allows us to probe chromosome encounter dynamics between different loci pairs across the cell cycle. We also conduct two functional tests of CICI. We perturb the chromosome conformation near a DNA double-strand break and observe altered donor preference in homologous recombination; we force interactions between early and late-firing DNA replication origins and find no significant changes in replication timing. These results suggest that chromosome conformation plays a deterministic role in homology-directed DNA repair, but not in the establishment of replication timing. Overall, our study demonstrates that CICI is a powerful tool to study chromosome dynamics and 3D genome function.

Methods to selectively manipulate specific long-distance chromosomal interactions are limited. Here the authors develop a method called Chemically Induced Chromosomal Interaction (CICI) to engineer interactions and demonstrate that 3D conformation plays a causal role in establishing donor DNA preference during DNA repair.

Multiscale modelling of the extracellular matrix

The extracellular matrix is a complex three-dimensional network of molecules that provides cells with a complex microenvironment. The major constituents of the extracellular matrix such as collagen, elastin and associated proteins form supramolecular assemblies contributing to its physicochemical properties and organization. The structure of proteins and their supramolecular assemblies such as fibrils have been studied at the atomic level (e.g., by X-ray crystallography, Nuclear Magnetic Resonance and cryo-Electron Microscopy) or at the microscopic scale. However, many protein complexes are too large to be studied at the atomic level and too small to be studied by microscopy. Most extracellular matrix components fall into this intermediate scale, so-called the mesoscopic scale, preventing their detailed characterization. Simulation and modelling are some of the few powerful and promising approaches that can deepen our understanding of mesoscale systems. We have developed a set of modelling tools to study the self-organization of the extracellular matrix and large motion of macromolecules at the mesoscale level by taking advantage of the dynamics of articulated rigid bodies as a mean to study a larger range of motions at the cost of atomic resolution.

The Dynamic Behavior of Chromatin in Response to DNA Double-Strand Breaks

The primary functions of the eukaryotic nucleus as a site for the storage, retrieval, and replication of information require a highly dynamic chromatin organization, which can be affected by the presence of DNA damage. In response to double-strand breaks (DSBs), the mobility of chromatin at the break site is severely affected and, to a lesser extent, that of other chromosomes. The how and why of such movement has been widely studied over the last two decades, leading to different mechanistic models and proposed potential roles underlying both local and global mobility. Here, we review the state of the knowledge on current issues affecting chromatin mobility upon DSBs, and highlight its role as a crucial step in the DNA damage response (DDR).

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.

High-Resolution Microscopy to Learn the Nuclear Organization of the Living Yeast Cells

The spatial organization of the nucleus is a key determinant in all genome activities. However, the accurate measurement of the nuclear organization is still technically challenging. Here, the technology NucQuant we created previously was utilized to detect the variation of the nuclear organization, including the heterogeneity of the nuclear geometry, the change of the NPC distribution along different cell cycle stages during interphase, and the organization of the nucleolus. The results confirmed that not only the growth rate and the NPC distribution are influenced by the carbon source; the nuclear shape is also impacted by the carbon source. The nuclei lost their spherical geometry gradually when the cell was cultured from the most to a less favorable carbon source. We also discovered that the nucleolus prefers to locate at the nuclear periphery, which was called the "genes poor region," especially when the cells entered quiescence. Furthermore, the distribution of the NPC along the different stages during the interphase was analyzed. We proposed that with the growth of the cell, the nucleus would grow from the surface of the NE flanking the nucleolus firstly.

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.

Organoids: A new approach in toxicity testing of nanotherapeutics

Nanotechnology has revolutionized diverse fields, which include agriculture, the consumer market, medicine, and other fields. Widespread use of nanotechnology-based products has led to increased prevalence of these novel formulations in the environment, which has raised concerns regarding their deleterious effects. The application of nanotechnology-based formulations into clinical use is hampered by the lack of the availability of effective in vitro systems, which could accurately assess their in vivo toxic effects. A plethora of studies has shown the hazardous effects of nanoparticle-based formulations in two-dimensional in vitro cell cultures and animal models. These have some associated disadvantages when used for the evaluation of nano-toxicity. Organoid technology fills the space between existing two-dimensional cell line culture and in vivo models. The uniqueness of organoids over other systems for evaluating toxicity caused by nano-drug formulation includes them being a co-culture of diverse cell types, dynamic flow within them that simulates the actual flow of nanoparticles within biological systems, extensive cell-cell, cell-matrix interactions, and a tissue-like morphology. Thus, it mimics the actual tissue microenvironment and, subsequently, provides an opportunity to study drug metabolism and toxico-dynamics of nanotechnology-based novel formulations. The use of organoids in the evaluation of nano-drug toxicity is in its infancy. A limited number of studies conducted so far have shown good predictive value and efficiently significant data correlation with the clinical trials. In this review, we attempt to introduce organoids of the liver, lungs, brain, kidney intestine, and potential applications to evaluate toxicity caused by nanoparticles.

The rDNA is biomolecular condensate formed by polymer-polymer phase separation and is sequestered in the nucleolus by transcription and R-loops

The nucleolus is the site of ribosome biosynthesis encompassing the ribosomal DNA (rDNA) locus in a phase separated state within the nucleus. In budding yeast, we find the rDNA locus and Cdc14, a protein phosphatase that co-localizes with the rDNA, behave like a condensate formed by polymer-polymer phase separation, while ribonucleoproteins behave like a condensate formed by liquid-liquid phase separation. The compaction of the rDNA and Cdc14's nucleolar distribution are dependent on the concentration of DNA cross-linkers. In contrast, ribonucleoprotein nucleolar distribution is independent of the concentration of DNA cross-linkers and resembles droplets in vivo upon replacement of the endogenous rDNA locus with high-copy plasmids. When ribosomal RNA is transcribed from the plasmids by Pol II, the rDNA-binding proteins and ribonucleoprotein signals are weakly correlated, but upon repression of transcription, ribonucleoproteins form a single, stable droplet that excludes rDNA-binding proteins from its center. Degradation of RNA-DNA hybrid structures, known as R-loops, by overexpression of RNase H1 results in the physical exclusion of the rDNA locus from the nucleolar center. Thus, the rDNA locus is a polymer-polymer phase separated condensate that relies on transcription and physical contact with RNA transcripts to remain encapsulated within the nucleolus.

Polymer modelling unveils the roles of heterochromatin and nucleolar organizing regions in shaping 3D genome organization in Arabidopsis thaliana

The 3D genome is characterized by a complex organization made of genomic and epigenomic layers with profound implications on gene regulation and cell function. However, the understanding of the fundamental mechanisms driving the crosstalk between nuclear architecture and (epi)genomic information is still lacking. The plant Arabidopsis thaliana is a powerful model organism to address these questions owing to its compact genome for which we have a rich collection of microscopy, chromosome conformation capture (Hi-C) and ChIP-seq experiments. Using polymer modelling, we investigate the roles of nucleolus formation and epigenomics-driven interactions in shaping the 3D genome of A. thaliana. By validation of several predictions with published data, we demonstrate that self-attracting nucleolar organizing regions and repulsive constitutive heterochromatin are major mechanisms to regulate the organization of chromosomes. Simulations also suggest that interphase chromosomes maintain a partial structural memory of the V-shapes, typical of (sub)metacentric chromosomes in anaphase. Additionally, self-attraction between facultative heterochromatin regions facilitates the formation of Polycomb bodies hosting H3K27me3-enriched gene-clusters. Since nucleolus and heterochromatin are highly-conserved in eukaryotic cells, our findings pave the way for a comprehensive characterization of the generic principles that are likely to shape and regulate the 3D genome in many species.

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.

G1/S transcription factors assemble in increasing numbers of discrete clusters through G1 phase

In budding yeast, the transcription factors SBF and MBF activate a large program of gene expression in late G1 phase that underlies commitment to cell division, termed Start. SBF/MBF are limiting with respect to target promoters in small G1 phase cells and accumulate as cells grow, raising the questions of how SBF/MBF are dynamically distributed across the G1/S regulon and how this impacts the Start transition. Super-resolution Photo-Activatable Localization Microscopy (PALM) mapping of the static positions of SBF/MBF subunits in fixed cells revealed each transcription factor was organized into discrete clusters containing approximately eight copies regardless of cell size and that the total number of clusters increased as cells grew through G1 phase. Stochastic modeling using reasonable biophysical parameters recapitulated growth-dependent SBF/MBF clustering and predicted TF dynamics that were confirmed in live cell PALM experiments. This spatio-temporal organization of SBF/MBF may help coordinate activation of G1/S regulon and the Start transition.

Complex Chromatin Motions for DNA Repair

A number of studies across different model systems revealed that chromatin undergoes significant changes in dynamics in response to DNA damage. These include local motion changes at damage sites, increased nuclear exploration of both damaged and undamaged loci, and directed motions to new nuclear locations associated with certain repair pathways. These studies also revealed the need for new analytical methods to identify directed motions in a context of mixed trajectories, and the importance of investigating nuclear dynamics over different time scales to identify diffusion regimes. Here we provide an overview of the current understanding of this field, including imaging and analytical methods developed to investigate nuclear dynamics in different contexts. These dynamics are essential for genome integrity. Identifying the molecular mechanisms responsible for these movements is key to understanding how their misregulation contributes to cancer and other genome instability disorders.

Quantitative Analysis of Spatial Distributions of All tRNA Genes in Budding Yeast

In the budding yeast nucleus, transfer RNA (tRNA) genes are considered to localize in the vicinity of the nucleolus; however, the use of Hi-C and fluorescent repressor-operator system techniques has clearly indicated that the tRNA genes are distributed not only around the nucleolus but also at other nuclear locations. However, there are some discrepancies between Hi-C data analysis and the results indicated from fluorescence microscopy data. To fill these gaps, we systematically clarified the spatial arrangements of all tRNA genes in the budding yeast nucleus using the genome simulation model developed by us. The simulation results revealed that out of 275 tRNA genes, 58% were found to be spatially distributed around the centromeres, 16% were distributed around the ribosomal DNA regions, and the remaining 26% were distributed between the centromeres and ribosomal DNA regions. Furthermore, 1% of all tRNA genes were found to be spatially distributed around the nuclear envelope, 30% were distributed around the center of the nucleus, and the remaining 69% were distributed between the nuclear envelope and the center of the nucleus. The percentage distributions were highly similar to those of the 176 tRNA genes encoding tRNAs having an anticodon for the optimal codons. The simulation results also revealed that the spatial arrangements of tRNA genes were affected by linear genomic distance from the tethering elements such as the centromeres or telomeres; however, the distance was only one of the factors to determine spatial distribution. This study also investigates whether tRNA gene transcriptional levels depend on the arrangements in the budding yeast nucleus by integrating the genome simulation model with tRNA sequencing data. The results suggest that the transcriptional levels did not depend on the arrangements in the nucleus. By using the genome simulation model, we showed the possibility of quantitatively analyzing genome structures.

Impact of Chromosome Fusions on 3D Genome Organization and Gene Expression in Budding Yeast

The three-dimensional (3D) organization of chromosomes can influence transcription. However, the frequency and magnitude of these effects remain debated. To determine how changes in chromosome positioning affect transcription across thousands of genes with minimal perturbation, we characterized nuclear organization and global gene expression in budding yeast containing chromosome fusions. We used computational modeling and single-cell imaging to determine chromosome positions, and integrated these data with genome-wide transcriptional profiles from RNA sequencing. We find that chromosome fusions dramatically alter 3D nuclear organization without leading to strong genome-wide changes in transcription. However, we observe a mild but significant and reproducible increase in the expression of genes displaced away from the periphery. The increase in transcription is inversely proportional to the propensity of a given locus to be at the nuclear periphery; for example, a 10% decrease in the propensity of a gene to reside at the nuclear envelope is accompanied by a 10% increase in gene expression. Modeling suggests that this is due to both deletion of telomeres and to displacement of genes relative to the nuclear periphery. These data suggest that basal transcriptional activity is sensitive to radial changes in gene position, and provide insight into the functional relevance of budding yeast chromosome-level 3D organization in gene expression.

Chromosome Conformation Capture and Beyond: Toward an Integrative View of Chromosome Structure and Function

Rapidly developing technologies have recently fueled an exciting era of discovery in the field of chromosome structure and nuclear organization. In addition to chromosome conformation capture (3C) methods, new alternative techniques have emerged to study genome architecture and biological processes in the nucleus, often in single or living cells. This sets an unprecedented stage for exploring the mechanisms that link chromosome structure and biological function. Here we review popular as well as emerging approaches to study chromosome organization, focusing on the contribution of complementary methodologies to our understanding of structures revealed by 3C methods and their biological implications, and discuss the next technical and conceptual frontiers.

Common Features of the Pericentromere and Nucleolus

Both the pericentromere and the nucleolus have unique characteristics that distinguish them amongst the rest of genome. Looping of pericentromeric DNA, due to structural maintenance of chromosome (SMC) proteins condensin and cohesin, drives its ability to maintain tension during metaphase. Similar loops are formed via condensin and cohesin in nucleolar ribosomal DNA (rDNA). Condensin and cohesin are also concentrated in transfer RNA (tRNA) genes, genes which may be located within the pericentromere as well as tethered to the nucleolus. Replication fork stalling, as well as downstream consequences such as genomic recombination, are characteristic of both the pericentromere and rDNA. Furthermore, emerging evidence suggests that the pericentromere may function as a liquid-liquid phase separated domain, similar to the nucleolus. We therefore propose that the pericentromere and nucleolus, in part due to their enrichment of SMC proteins and others, contain similar domains that drive important cellular activities such as segregation, stability, and repair.

AI-Assisted Forward Modeling of Biological Structures

The rise of machine learning and deep learning technologies have allowed researchers to automate image classification. We describe a method that incorporates automated image classification and principal component analysis to evaluate computational models of biological structures. We use a computational model of the kinetochore to demonstrate our artificial-intelligence (AI)-assisted modeling method. The kinetochore is a large protein complex that connects chromosomes to the mitotic spindle to facilitate proper cell division. The kinetochore can be divided into two regions: the inner kinetochore, including proteins that interact with DNA; and the outer kinetochore, comprised of microtubule-binding proteins. These two kinetochore regions have been shown to have different distributions during metaphase in live budding yeast and therefore act as a test case for our forward modeling technique. We find that a simple convolutional neural net (CNN) can correctly classify fluorescent images of inner and outer kinetochore proteins and show a CNN trained on simulated, fluorescent images can detect difference in experimental images. A polymer model of the ribosomal DNA locus serves as a second test for the method. The nucleolus surrounds the ribosomal DNA locus and appears amorphous in live-cell, fluorescent microscopy experiments in budding yeast, making detection of morphological changes challenging. We show a simple CNN can detect subtle differences in simulated images of the ribosomal DNA locus, demonstrating our CNN-based classification technique can be used on a variety of biological structures.

Quantification of the dynamic behaviour of ribosomal DNA genes and nucleolus during yeast Saccharomyces cerevisiae cell cycle

Spatial organisation of chromosomes is a determinant of genome stability and is required for proper mitotic segregation. However, visualization of individual chromatids in living cells and quantification of their geometry, remains technically challenging. Here, we used live cell imaging to quantitate the three-dimensional conformation of yeast Saccharomyces cerevisiae ribosomal DNA (rDNA). rDNA is confined within the nucleolus and is composed of about 200 copies representing about 10% of the yeast genome. To fluorescently label rDNA in living cells, we generated a set of nucleolar proteins fused to GFP or made use of a tagged rDNA, in which lacO repetitions were inserted in each repeat unit. We could show that nucleolus is not modified in appearance, shape or size during interphase while rDNA is highly reorganized. Computationally tracing 3D rDNA paths allowed us to quantitatively assess rDNA size, shape and geometry. During interphase, rDNA was progressively reorganized from a zig-zag segmented line of small size (5,5 µm) to a long, homogeneous, line-like structure of 8,7 µm in metaphase. Most importantly, whatever the cell-cycle stage considered, rDNA fibre could be decomposed in subdomains, as previously suggested for 3D chromatin organisation. Finally, we could determine that spatial reorganisation of these subdomains and establishment of rDNA mitotic organisation is under the control of the cohesin complex.

Principles of meiotic chromosome assembly revealed in S. cerevisiae

During meiotic prophase, chromosomes organise into a series of chromatin loops emanating from a proteinaceous axis, but the mechanisms of assembly remain unclear. Here we use Saccharomyces cerevisiae to explore how this elaborate three-dimensional chromosome organisation is linked to genomic sequence. As cells enter meiosis, we observe that strong cohesin-dependent grid-like Hi-C interaction patterns emerge, reminiscent of mammalian interphase organisation, but with distinct regulation. Meiotic patterns agree with simulations of loop extrusion with growth limited by barriers, in which a heterogeneous population of expanding loops develop along the chromosome. Importantly, CTCF, the factor that imposes similar features in mammalian interphase, is absent in S. cerevisiae, suggesting alternative mechanisms of barrier formation. While grid-like interactions emerge independently of meiotic chromosome synapsis, synapsis itself generates additional compaction that matures differentially according to telomere proximity and chromosome size. Collectively, our results elucidate fundamental principles of chromosome assembly and demonstrate the essential role of cohesin within this evolutionarily conserved process.

From dynamic chromatin architecture to DNA damage repair and back

Maintaining the integrity of the genome in the face of DNA damage is crucial to ensure the survival of the cell and normal development. DNA lesions and repair occur in the context of the chromatin fiber, whose 3D organization and movements in the restricted volume of the nucleus are under intense scrutiny. Here, we highlight work from our and other labs that addresses how the dynamic organization of the chromatin fiber affects the repair of damaged DNA and how, conversely, DNA damage and repair affect the structure and dynamics of chromatin in the budding yeast nucleus.

Transient crosslinking kinetics optimize gene cluster interactions

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions.

Nucleosome positions alone can be used to predict domains in yeast chromosomes

DNA is packaged into chromosomes, which are further organized into domains: Regions of the genome which are more likely to self-interact. Domains have been observed in species ranging from bacteria to humans and are thought to play an important role in gene regulation. Yet the mechanisms of domain formation are not fully understood. Here we use computer simulations to investigate domain formation in yeast. Our model reproduces the experimentally observed domains using only nucleosome positioning information as an input, implying that (unlike in higher eukaryotes) domain boundary locations are largely determined at this level. Our results reveal how irregular nucleosome spacing impacts the 3D chromosome organization, pointing to a direct link between nucleosome positioning and genome regulation at the large scale.

We use molecular dynamics simulations based on publicly available micrococcal nuclease sequencing data for nucleosome positions to predict the 3D structure of chromatin in the yeast genome. Our main aim is to shed light on the mechanism underlying the formation of chromosomal interaction domains, chromosome regions of around 0.5 to 10 kbp which show enriched self-interactions, which were experimentally observed in recent MicroC experiments (importantly these are at a different length scale from the 100- to 1,000-kbp–sized domains observed in higher eukaryotes). We show that the sole input of nucleosome positioning data is already sufficient to determine the patterns of chromatin interactions and domain boundaries seen experimentally to a high degree of accuracy. Since the nucleosome spacing so strongly affects the larger-scale domain structure, we next examine the genome-wide linker-length distribution in more detail, finding that it is highly irregular and varies in different genomic regions such as gene bodies, promoters, and active and inactive genes. Finally we use our simple simulation model to characterize in more detail how irregular nucleosome spacing may affect local chromatin structure.

Rouse model with transient intramolecular contacts on a timescale of seconds recapitulates folding and fluctuation of yeast chromosomes

DNA folding and dynamics along with major nuclear functions are determined by chromosome structural properties, which remain, thus far, elusive in vivo. Here, we combine polymer modeling and single particle tracking experiments to determine the physico-chemical parameters of chromatin in vitro and in living yeast. We find that the motion of reconstituted chromatin fibers can be recapitulated by the Rouse model using mechanical parameters of nucleosome arrays deduced from structural simulations. Conversely, we report that the Rouse model shows some inconsistencies to analyze the motion and structural properties inferred from yeast chromosomes determined with chromosome conformation capture techniques (specifically, Hi-C). We hence introduce the Rouse model with Transient Internal Contacts (RouseTIC), in which random association and dissociation occurs along the chromosome contour. The parametrization of this model by fitting motion and Hi-C data allows us to measure the kinetic parameters of the contact formation reaction. Chromosome contacts appear to be transient; associated to a lifetime of seconds and characterized by an attractive energy of -0.3 to -0.5 kBT. We suggest attributing this energy to the occurrence of histone tail-DNA contacts and notice that its amplitude sets chromosomes in 'theta' conditions, in which they are poised for compartmentalization and phase separation.

How the Genome Folds: The Biophysics of Four-Dimensional Chromatin Organization

The genetic information that instructs transcription and other cellular functions is carried by the chromosomes, polymers of DNA in complex with histones and other proteins. These polymers are folded inside nuclei five orders of magnitude smaller than their linear length, and many facets of this folding correlate with or are causally related to transcription and other cellular functions. Recent advances in sequencing and imaging-based techniques have enabled new views into several layers of chromatin organization. These experimental findings are accompanied by computational modeling efforts based on polymer physics that can provide mechanistic insights and quantitative predictions. Here, we review current knowledge of the main levels of chromatin organization, from the scale of nucleosomes to the entire nucleus, our current understanding of their underlying biophysical and molecular mechanisms, and some of their functional implications.

Computational methods for analyzing and modeling genome structure and organization

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

Bottom-up modeling of chromatin segregation due to epigenetic modifications

Predicting how epigenetic marks control the 3D organization of the genome is key to understanding how these marks regulate gene expression. We show that a physical model of a chromosome with experimentally measured local interactions segregates into euchromatin- and heterochromatin-like phases. The model reproduces many of the features of the large-scale organization of the chromosome as measured by Hi-C. Our work provides an estimate of the amount of epigenetic marking needed to segregate a gene into heterochromatin.

We use a chromosome-scale simulation to show that the preferential binding of heterochromatin protein 1 (HP1) to regions high in histone methylation (specifically H3K9me3) results in phase segregation and reproduces features of the observed Hi-C contact map. Specifically, we perform Monte Carlo simulations with one computational bead per nucleosome and an H3K9me3 pattern based on published ChIP-seq signals. We implement a binding model in which HP1 preferentially binds to trimethylated histone tails and then oligomerizes to bridge together nucleosomes. We observe a phase reminiscent of heterochromatin—dense and high in H3K9me3—and another reminiscent of euchromatin—less dense and lacking H3K9me3. This segregation results in a plaid contact probability map that matches the general shape and position of published Hi-C data. Analysis suggests that a roughly 20-kb segment of H3K9me3 enrichment is required to drive segregation into the heterochromatic phase.

Sim3C: simulation of Hi-C and Meta3C proximity ligation sequencing technologies

Background

Chromosome conformation capture (3C) and Hi-C DNA sequencing methods have rapidly advanced our understanding of the spatial organization of genomes and metagenomes. Many variants of these protocols have been developed, each with their own strengths. Currently there is no systematic means for simulating sequence data from this family of sequencing protocols, potentially hindering the advancement of algorithms to exploit this new datatype.

Findings

We describe a computational simulator that, given simple parameters and reference genome sequences, will simulate Hi-C sequencing on those sequences. The simulator models the basic spatial structure in genomes that is commonly observed in Hi-C and 3C datasets, including the distance-decay relationship in proximity ligation, differences in the frequency of interaction within and across chromosomes, and the structure imposed by cells. A means to model the 3D structure of randomly generated topologically associating domains is provided. The simulator considers several sources of error common to 3C and Hi-C library preparation and sequencing methods, including spurious proximity ligation events and sequencing error.

Conclusions

We have introduced the first comprehensive simulator for 3C and Hi-C sequencing protocols. We expect the simulator to have use in testing of Hi-C data analysis algorithms, as well as more general value for experimental design, where questions such as the required depth of sequencing, enzyme choice, and other decisions can be made in advance in order to ensure adequate statistical power with respect to experimental hypothesis testing.

Characterizing meiotic chromosomes' structure and pairing using a designer sequence optimized for Hi-C

In chromosome conformation capture experiments (Hi-C), the accuracy with which contacts are detected varies due to the uneven distribution of restriction sites along genomes. In addition, repeated sequences or homologous regions remain indistinguishable because of the ambiguities they introduce during the alignment of the sequencing reads. We addressed both limitations by designing and engineering 144 kb of a yeast chromosome with regularly spaced restriction sites (Syn-HiC design). In the Syn-HiC region, Hi-C signal-to-noise ratio is enhanced and can be used to measure the shape of an unbiased distribution of contact frequencies, allowing to propose a robust definition of a Hi-C experiment resolution. The redesigned region is also distinguishable from its native homologous counterpart in an otherwise isogenic diploid strain. As a proof of principle, we tracked homologous chromosomes during meiotic prophase in synchronized and pachytene-arrested cells and captured important features of their spatial reorganization, such as chromatin restructuration into arrays of Rec8-delimited loops, centromere declustering, individualization, and pairing. Overall, we illustrate the promises held by redesigning genomic regions to explore complex biological questions.

Mesoscopic Rigid Body Modelling of the Extracellular Matrix Self-Assembly

The extracellular matrix (ECM) plays an important role in supporting tissues and organs. It even has a functional role in morphogenesis and differentiation by acting as a source of active molecules (matrikines). Many diseases are linked to dysfunction of ECM components and fragments or changes in their structures. As such it is a prime target for drugs. Because of technological limitations for observations at mesoscopic scales, the precise structural organisation of the ECM is not well-known, with sparse or fuzzy experimental observables. Based on the Unity3D game and physics engines, along with rigid body dynamics, we propose a virtual sandbox to model large biological molecules as dynamic chains of rigid bodies interacting together to gain insight into ECM components behaviour in the mesoscopic range. We have preliminary results showing how parameters such as fibre flexibility or the nature and number of interactions between molecules can induce different structures in the basement membrane. Using the Unity3D game engine and virtual reality headset coupled with haptic controllers, we immerse the user inside the corresponding simulation. Untrained users are able to navigate a complex virtual sandbox crowded with large biomolecules models in a matter of seconds.

A maximum-entropy model for predicting chromatin contacts

The packaging of DNA inside a nucleus shows complex structure stabilized by a host of DNA-bound factors. Both the distribution of these factors and the contacts between different genomic locations of the DNA can now be measured on a genome-wide scale. This has advanced the development of models aimed at predicting the conformation of DNA given only the locations of bound factors-the chromatin folding problem. Here we present a maximum-entropy model that is able to predict a contact map representation of structure given a sequence of bound factors. Non-local effects due to the sequence neighborhood around contacting sites are found to be important for making accurate predictions. Lastly, we show that the model can be used to infer a sequence of bound factors given only a measurement of structure. This opens up the possibility for efficiently predicting sequence regions that may play a role in generating cell-type specific structural differences.

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.

Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus

Regions of highly repetitive DNA, such as those found in the nucleolus, show a self-organization that is marked by spatial segregation and frequent self-interaction. The mechanisms that underlie the sequestration of these sub-domains are largely unknown. Using a stochastic, bead-spring representation of chromatin in budding yeast, we find enrichment of protein-mediated, dynamic chromosomal cross-links recapitulates the segregation, morphology and self-interaction of the nucleolus. Rates and enrichment of dynamic crosslinking have profound consequences on domain morphology. Our model demonstrates the nucleolus is phase separated from other chromatin in the nucleus and predicts that multiple rDNA loci will form a single nucleolus independent of their location within the genome. Fluorescent labeling of budding yeast nucleoli with CDC14-GFP revealed that a split rDNA locus indeed forms a single nucleolus. We propose that nuclear sub-domains, such as the nucleolus, result from phase separations within the nucleus, which are driven by the enrichment of protein-mediated, dynamic chromosomal crosslinks.

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.

Chromatin stiffening underlies enhanced locus mobility after DNA damage in budding yeast

DNA double-strand breaks (DSBs) induce a cellular response that involves histone modifications and chromatin remodeling at the damaged site and increases chromosome dynamics both locally at the damaged site and globally in the nucleus. In parallel, it has become clear that the spatial organization and dynamics of chromosomes can be largely explained by the statistical properties of tethered, but randomly moving, polymer chains, characterized mainly by their rigidity and compaction. How these properties of chromatin are affected during DNA damage remains, however, unclear. Here, we use live cell microscopy to track chromatin loci and measure distances between loci on yeast chromosome IV in thousands of cells, in the presence or absence of genotoxic stress. We confirm that DSBs result in enhanced chromatin subdiffusion and show that intrachromosomal distances increase with DNA damage all along the chromosome. Our data can be explained by an increase in chromatin rigidity, but not by chromatin decondensation or centromeric untethering only. We provide evidence that chromatin stiffening is mediated in part by histone H2A phosphorylation. Our results support a genome-wide stiffening of the chromatin fiber as a consequence of DNA damage and as a novel mechanism underlying increased chromatin mobility.

SMC complexes differentially compact mitotic chromosomes according to genomic context

Structural maintenance of chromosomes (SMC) protein complexes are key determinants of chromosome conformation. Using Hi-C and polymer modelling, we study how cohesin and condensin, two deeply conserved SMC complexes, organize chromosomes in the budding yeast Saccharomyces cerevisiae. The canonical role of cohesin is to co-align sister chromatids, while condensin generally compacts mitotic chromosomes. We find strikingly different roles for the two complexes in budding yeast mitosis. First, cohesin is responsible for compacting mitotic chromosome arms, independently of sister chromatid cohesion. Polymer simulations demonstrate that this role can be fully accounted for through cis-looping of chromatin. Second, condensin is generally dispensable for compaction along chromosome arms. Instead, it plays a targeted role compacting the rDNA proximal regions and promoting resolution of peri-centromeric regions. Our results argue that the conserved mechanism of SMC complexes is to form chromatin loops and that distinct SMC-dependent looping activities are selectively deployed to appropriately compact chromosomes.

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.

3D clustering of co-regulated genes and its effect on gene expression

There are extensive long-distance chromosomal interactions in eukaryotic genomes, but to what extent these interactions affect gene expression is not clear. Recent works have identified several cases where clustering of co-regulated genes leads to enhanced gene expression in budding yeast. Similar phenomenon was also observed in mammalian cells. These results challenge widely held views of gene regulation in yeast and further our understanding of how the 3D organization of the genome contribute to gene regulation in eukaryotes.