Dynamical modeling of three-dimensional genome organization in interphase budding yeast

Nonequilibrium switching of segmental states can influence compaction of chromatin

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

3D models of fungal chromosomes to enhance visual integration of omics data

The functions of eukaryotic chromosomes and their spatial architecture in the nucleus are reciprocally dependent. Hi-C experiments are routinely used to study chromosome 3D organization by probing chromatin interactions. Standard representation of the data has relied on contact maps that show the frequency of interactions between parts of the genome. In parallel, it has become easier to build 3D models of the entire genome based on the same Hi-C data, and thus benefit from the methodology and visualization tools developed for structural biology. 3D modeling of entire genomes leverages the understanding of their spatial organization. However, this opportunity for original and insightful modeling is underexploited. In this paper, we show how seeing the spatial organization of chromosomes can bring new perspectives to omics data integration. We assembled state-of-the-art tools into a workflow that goes from Hi-C raw data to fully annotated 3D models and we re-analysed public omics datasets available for three fungal species. Besides the well-described properties of the spatial organization of their chromosomes (Rabl conformation, hypercoiling and chromosome territories), our results highlighted (i) in Saccharomyces cerevisiae, the backbones of the cohesin anchor regions, which were aligned all along the chromosomes, (ii) in Schizosaccharomyces pombe, the oscillations of the coiling of chromosome arms throughout the cell cycle and (iii) in Neurospora crassa, the massive relocalization of histone marks in mutants of heterochromatin regulators. 3D modeling of the chromosomes brings new opportunities for visual integration of omics data. This holistic perspective supports intuition and lays the foundation for building new concepts.

Large-scale data-driven and physics-based models offer insights into the relationships among the structures, dynamics, and functions of chromosomes

The organized three-dimensional chromosome architecture in the cell nucleus provides scaffolding for precise regulation of gene expression. When the cell changes its identity in the cell-fate decision-making process, extensive rearrangements of chromosome structures occur accompanied by large-scale adaptations of gene expression, underscoring the importance of chromosome dynamics in shaping genome function. Over the last two decades, rapid development of experimental methods has provided unprecedented data to characterize the hierarchical structures and dynamic properties of chromosomes. In parallel, these enormous data offer valuable opportunities for developing quantitative computational models. Here, we review a variety of large-scale polymer models developed to investigate the structures and dynamics of chromosomes. Different from the underlying modeling strategies, these approaches can be classified into data-driven ('top-down') and physics-based ('bottom-up') categories. We discuss their contributions to offering valuable insights into the relationships among the structures, dynamics, and functions of chromosomes and propose the perspective of developing data integration approaches from different experimental technologies and multidisciplinary theoretical/simulation methods combined with different modeling strategies.

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.

Insights into the cell fate decision-making processes from chromosome structural reorganizations

The cell fate decision-making process, which provides the capability of a cell transition to a new cell type, involves the reorganizations of 3D genome structures. Currently, the high temporal resolution picture of how the chromosome structural rearrangements occur and further influence the gene activities during the cell-state transition is still challenging to acquire. Here, we study the chromosome structural reorganizations during the cell-state transitions among the pluripotent embryonic stem cell, the terminally differentiated normal cell, and the cancer cell using a nonequilibrium landscape-switching model implemented in the molecular dynamics simulation. We quantify the chromosome (de)compaction pathways during the cell-state transitions and find that the two pathways having the same destinations can merge prior to reaching the final states. The chromosomes at the merging states have similar structural geometries but can differ in long-range compartment segregation and spatial distribution of the chromosomal loci and genes, leading to cell-type-specific transition mechanisms. We identify the irreversible pathways of chromosome structural rearrangements during the forward and reverse transitions connecting the same pair of cell states, underscoring the critical roles of nonequilibrium dynamics in the cell-state transitions. Our results contribute to the understanding of the cell fate decision-making processes from the chromosome structural perspective.

Quantifying Chromosome Structural Reorganizations during Differentiation, Reprogramming, and Transdifferentiation

We developed a nonequilibrium model to study chromosome structural reorganizations within a simplified cell developmental system. From the chromosome structural perspective, we predicted that the neural progenitor cell is on the neural developmental path and very close to the transdifferentiation path from the fibroblast to the neuron cell. We identified an early bifurcation of stem cell differentiation processes and the cell-of-origin-specific reprogramming pathways. Our theoretical results are in good agreement with available experimental evidence, promoting future applications of our approach.

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

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

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.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

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.

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.

Conformational state switching and pathways of chromosome dynamics in cell cycle

The cell cycle is a process and function of a cell with different phases essential for cell growth, proliferation, and replication. It depends on the structure and dynamics of the underlying DNA molecule, which underpins the genome function. A microscopic structural-level understanding of how a genome or its functional module chromosome performs the cell cycle in terms of large-scale conformational transformation between different phases, such as the interphase and the mitotic phase, is still challenging. Here, we develop a non-equilibrium, excitation-relaxation energy landscape-switching model to quantify the underlying chromosome conformational transitions through (de-)condensation for a complete microscopic understanding of the cell cycle. We show that the chromosome conformational transition mechanism from the interphase to the mitotic phase follows a two-stage scenario, in good agreement with the experiments. In contrast, the mitotic exit pathways show the existence of an over-expanded chromosome that recapitulates the chromosome in the experimentally identified intermediate state at the telophase. We find the conformational pathways are heterogeneous and irreversible as a result of the non-equilibrium dynamics of the cell cycle from both structural and kinetic perspectives. We suggest that the irreversibility is mainly due to the distinct participation of the ATP-dependent structural maintenance of chromosomal protein complexes during the cell cycle. Our findings provide crucial insights into the microscopic molecular structural and dynamical physical mechanism for the cell cycle beyond the previous more macroscopic descriptions. Our non-equilibrium landscape framework is general and applicable to study diverse non-equilibrium physical and biological processes such as active matter, differentiation/development, and cancer.

Toward understanding the dynamic state of 3D genome

The three-dimensional (3D) genome organization and its role in biological activities have been investigated for over a decade in the field of cell biology. Recent studies using live-imaging and polymer simulation have suggested that the higher-order chromatin structures are dynamic; the stochastic fluctuations of nucleosomes and genomic loci cannot be captured by bulk-based chromosome conformation capture techniques (Hi-C). In this review, we focus on the physical nature of the 3D genome architecture. We first describe how to decode bulk Hi-C data with polymer modeling. We then introduce our recently developed PHi-C method, a computational tool for modeling the fluctuations of the 3D genome organization in the presence of stochastic thermal noise. We also present another new method that analyzes the dynamic rheology property (represented as microrheology spectra) as a measure of the flexibility and rigidity of genomic regions over time. By applying these methods to real Hi-C data, we highlighted a temporal hierarchy embedded in the 3D genome organization; chromatin interaction boundaries are more rigid than the boundary interior, while functional domains emerge as dynamic fluctuations within a particular time interval. Our methods may bridge the gap between live-cell imaging and Hi-C data and elucidate the nature of the dynamic 3D genome organization.

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.

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.

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.

Physical principles and functional consequences of nuclear compartmentalization in budding yeast

One striking feature of eukaryotic nuclei is the existence of discrete regions, in which specific factors concentrate while others are excluded, thus forming microenvironments with different molecular compositions and biological functions. These domains are often referred to as subcompartments even though they are not membrane enclosed. Despite their functional importance the physical nature of these structures remains largely unknown. Here, we describe how the Saccharomyces cerevisiae nucleus is compartmentalized and discuss possible physical models underlying the formation and maintenance of chromatin associated subcompartments. Focusing on three particular examples, the nucleolus, silencing foci, and repair foci, we discuss the biological implications of these different models as well as possible approaches to challenge them in living cells.

Estimation of the Spatial Chromatin Structure Based on a Multiresolution Bead-Chain Model

We present a method to infer 3D chromatin configurations from Chromosome Conformation Capture data. Quite a few methods have been proposed to estimate the structure of the nuclear dna in homogeneous populations of cells from this kind of data. Many of them transform contact frequencies into euclidean distances between pairs of chromatin fragments, and then reconstruct the structure by solving a distance-to-geometry problem. To avoid inconsistencies, our method is based on a score function that does not require any frequency-to-distance translation. We propose a multiscale chromatin model where the chromatin fiber is suitably partitioned at each scale. The partial structures are estimated independently, and connected to rebuild the whole fiber. Our score function consists of a data-fit part and a penalty part, balanced automatically at each scale and each subchain. The penalty part enforces soft geometric constraints. As many different structures can fit the data, our sampling strategy produces a set of solutions with similar scores. The procedure contains a few parameters, independent of both the scale and the genomic segment treated. The partition of the fiber, along with intrinsically parallel parts, make this method computationally efficient. Results from human genome data support the biological plausibility of our solutions.

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.

Unfolding the Genome: The Case Study of P. falciparum

The development of new ways to probe samples for the three-dimensional (3D) structure of DNA paves the way for in depth and systematic analyses of the genome architecture. 3C-like methods coupled with high-throughput sequencing can now assess physical interactions between pairs of loci in a genome-wide fashion, thus enabling the creation of genome-by-genome contact maps. The spreading of such protocols creates many new opportunities for methodological development: how can we infer 3D models from these contact maps? Can such models help us gain insights into biological processes? Several recent studies applied such protocols to P. falciparum (the deadliest of the five human malaria parasites), assessing its genome organization at different moments of its life cycle. With its small genomic size, fairly simple (yet changing) genomic organization during its lifecyle and strong correlation between chromatin folding and gene expression, this parasite is the ideal case study for applying and developing methods to infer 3D models and use them for downstream analysis. Here, I review a set of methods used to build and analyse three-dimensional models from contact maps data with a special highlight on P. falciparum's genome organization.

ChromStruct 4: A Python Code to Estimate the Chromatin Structure from Hi-C Data

A method and a stand-alone Python(TM) code to estimate the 3D chromatin structure from chromosome conformation capture data are presented. The method is based on a multiresolution, modified-bead-chain chromatin model, evolved through quaternion operators in a Monte Carlo sampling. The solution space to be sampled is generated by a score function with a data-fit part and a constraint part where the available prior knowledge is implicitly coded. The final solution is a set of 3D configurations that are compatible with both the data and the prior knowledge. The iterative code, provided here as additional material, is equipped with a graphical user interface and stores its results in standard-format files for 3D visualization. We describe the mathematical-computational aspects of the method and explain the details of the code. Some experimental results are reported, with a demonstration of their fit to the data.

Chromosome-nuclear envelope attachments affect interphase chromosome territories and entanglement

Background

It is well recognized that the interphase chromatin of higher eukaryotes folds into non-random configurations forming territories within the nucleus. Chromosome territories have biologically significant properties, and understanding how these properties change with time during lifetime of the cell is important. Chromosome–nuclear envelope (Chr–NE) interactions play a role in epigenetic regulation of DNA replication, repair, and transcription. However, their role in maintaining chromosome territories remains unclear.

Results

We use coarse-grained molecular dynamics simulations to study the effects of Chr–NE interactions on the dynamics of chromosomes within a model of the Drosophila melanogaster regular (non-polytene) interphase nucleus, on timescales comparable to the duration of interphase. The model simulates the dynamics of chromosomes bounded by the NE. Initially, the chromosomes in the model are prearranged in fractal-like configurations with physical parameters such as nucleus size and chromosome persistence length taken directly from experiment. Time evolution of several key observables that characterize the chromosomes is quantified during each simulation: chromosome territories, chromosome entanglement, compactness, and presence of the Rabl (polarized) chromosome arrangement. We find that Chr–NE interactions help maintain chromosome territories by slowing down and limiting, but not eliminating, chromosome entanglement on biologically relevant timescales. At the same time, Chr–NE interactions have little effect on the Rabl chromosome arrangement as well as on how chromosome compactness changes with time. These results are rationalized by simple dimensionality arguments, robust to model details. All results are robust to the simulated activity of topoisomerase, which may be present in the interphase cell nucleus.

Conclusions

Our study demonstrates that Chr–NE attachments may help maintain chromosome territories, while slowing down and limiting chromosome entanglement on biologically relevant timescales. However, Chr–NE attachments have little effect on chromosome compactness or the Rabl chromosome arrangement.

Electronic supplementary material

The online version of this article (10.1186/s13072-018-0173-5) contains supplementary material, which is available to authorized users.

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.

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.

Inferring the physical properties of yeast chromatin through Bayesian analysis of whole nucleus simulations

Background

The structure and mechanical properties of chromatin impact DNA functions and nuclear architecture but remain poorly understood. In budding yeast, a simple polymer model with minimal sequence-specific constraints and a small number of structural parameters can explain diverse experimental data on nuclear architecture. However, how assumed chromatin properties affect model predictions was not previously systematically investigated.

Results

We used hundreds of dynamic chromosome simulations and Bayesian inference to determine chromatin properties consistent with an extensive dataset that includes hundreds of measurements from imaging in fixed and live cells and two Hi-C studies. We place new constraints on average chromatin fiber properties, narrowing down the chromatin compaction to ~53–65 bp/nm and persistence length to ~52–85 nm. These constraints argue against a 20–30 nm fiber as the exclusive chromatin structure in the genome. Our best model provides a much better match to experimental measurements of nuclear architecture and also recapitulates chromatin dynamics measured on multiple loci over long timescales.

Conclusion

This work substantially improves our understanding of yeast chromatin mechanics and chromosome architecture and provides a new analytic framework to infer chromosome properties in other organisms.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-017-1199-x) contains supplementary material, which is available to authorized users.

Heterogeneous Spatial Distribution of Transcriptional Activity in Budding Yeast Nuclei

Recent microscopic and simulation studies have shown that the genome structure fluctuates dynamically in the nuclei of budding yeast Saccharomyces cerevisiae. This genome-wide movement should lead to the fluctuations of individual genes in their territorial regions. This raises an intriguing question of whether the resulting distribution of genes is correlated to their transcriptional activity. An effective method for examining this correlation is to analyze how the spatial distribution of genes and their transcriptional activity are modified by mutation. In this study, we analyzed the modification observed in a budding yeast mutant in which genes necessary for anchoring telomeres to the nuclear envelope, yku70 and esc1, are silenced. Taddei et al. reported that 60 genes are clearly misregulated by this mutation, with 28 and 32 genes downregulated and upregulated, respectively. We calculated the probability density maps of the misregulated genes using a model of dynamical movement of the yeast genome in both wild-type (WT) and yku70 esc1 mutant and showed that the density of downregulated genes is larger near the nucleolus, whereas the density of upregulated genes is larger at the opposite side of the nucleus. By comparing these genes with those highly (top 200 of transcriptome) and lowly (bottom 200) expressed, we showed that the simulated distribution of 28 downregulated (12 out of 32 upregulated) genes has a distinctly larger overlap with the distribution of lowly (highly) expressed genes in the mutant than in the WT. The remaining 20 upregulated genes are localized near the nuclear envelope both in the WT and in the mutant. These results showed that the transcriptional level of genes is affected by their spatial distribution, thus highlighting the importance of the structural regulation in the yeast genome.

Physical Modeling of Dynamic Coupling between Chromosomal Loci

The motion of chromosomal DNA is essential to many biological processes, including segregation, transcriptional regulation, recombination, and packaging. Physical understanding of these processes would be dramatically enhanced through predictive, quantitative modeling of chromosome dynamics of multiple loci. Using a polymer dynamics framework, we develop a prediction for the correlation in the velocities of two loci on a single chromosome or otherwise connected by chromatin. These predictions reveal that the signature of correlated motion between two loci can be identified by varying the lag time between locus position measurements. In general, this theory predicts that as the lag time interval increases, the dual-loci dynamic behavior transitions from being completely uncorrelated to behaving as an effective single locus. This transition corresponds to the timescale of the stress communication between loci through the intervening segment. This relatively simple framework makes quantitative predictions based on a single timescale fit parameter that can be directly compared to the in vivo motion of fluorescently labeled chromosome loci. Furthermore, this theoretical framework enables the detection of dynamically coupled chromosome regions from the signature of their correlated motion.

Decoding the principles underlying the frequency of association with nucleoli for RNA polymerase III-transcribed genes in budding yeast

In budding yeast, RNA polymerase III–transcribed genes preferentially associate with the nucleolar and nuclear periphery when permitted by the Rabl-like orientation of interphase chromosomes.

The association of RNA polymerase III (Pol III)–transcribed genes with nucleoli seems to be an evolutionarily conserved property of the spatial organization of eukaryotic genomes. However, recent studies of global chromosome architecture in budding yeast have challenged this view. We used live-cell imaging to determine the intranuclear positions of 13 Pol III–transcribed genes. The frequency of association with nucleolus and nuclear periphery depends on linear genomic distance from the tethering elements—centromeres or telomeres. Releasing the hold of the tethering elements by inactivating centromere attachment to the spindle pole body or changing the position of ribosomal DNA arrays resulted in the association of Pol III–transcribed genes with nucleoli. Conversely, ectopic insertion of a Pol III–transcribed gene in the vicinity of a centromere prevented its association with nucleolus. Pol III–dependent transcription was independent of the intranuclear position of the gene, but the nucleolar recruitment of Pol III–transcribed genes required active transcription. We conclude that the association of Pol III–transcribed genes with the nucleolus, when permitted by global chromosome architecture, provides nucleolar and/or nuclear peripheral anchoring points contributing locally to intranuclear chromosome organization.

Mechanobiology of Chromatin and the Nuclear Interior

The view of the cell nucleus has evolved from an isolated, static organelle to a dynamic structure integrated with other mechanical elements of the cell. Both dynamics and integration appear to contribute to a mechanical regulation of genome expression. Here, we review physical structures inside the nucleus at different length scales and the dynamic reorganization modulated by cellular forces. First, we discuss nuclear organization focusing on self-assembly and disassembly of DNA structures and various nuclear bodies. We then discuss the importance of connections from the chromatin fiber through the nuclear envelope to the rest of the cell as they relate to mechanobiology. Finally, we discuss how cell stimulation, both chemical and physical, can alter nuclear structures and ultimately cellular function in healthy cells and in some model diseases. The view of chromatin and nuclear bodies as mechanical entities integrated with force generation from the cytoskeleton combines polymer physics with cell biology and medicine.

Quantified effects of chromosome-nuclear envelope attachments on 3D organization of chromosomes

We use a combined experimental and computational approach to study the effects of chromosome-nuclear envelope (Chr-NE) attachments on the 3D genome organization of Drosophila melanogaster (fruit fly) salivary gland nuclei. We consider 3 distinct models: a Null model - without specific Chr-NE attachments, a 15-attachment model - with 15 previously known Chr-NE attachments, and a 48-attachment model - with 15 original and 33 recently identified Chr-NE attachments. The radial densities of chromosomes in the models are compared to the densities observed in 100 experimental images of optically sectioned salivary gland nuclei forming "z-stacks." Most of the experimental z-stacks support the Chr-NE 48-attachment model suggesting that as many as 48 chromosome loci with appreciable affinity for the NE are necessary to reproduce the experimentally observed distribution of chromosome density in fruit fly nuclei. Next, we investigate if and how the presence and the number of Chr-NE attachments affect several key characteristics of 3D genome organization: chromosome territories and gene-gene contacts. This analysis leads to novel insight about the possible role of Chr-NE attachments in regulating the genome architecture. Specifically, we find that model nuclei with more numerous Chr-NE attachments form more distinct chromosome territories and their chromosomes intertwine less frequently. Intra-chromosome and intra-arm contacts are more common in model nuclei with Chr-NE attachments compared to the Null model (no specific attachments), while inter-chromosome and inter-arm contacts are less common in nuclei with Chr-NE attachments. We demonstrate that Chr-NE attachments increase the specificity of long-range inter-chromosome and inter-arm contacts. The predicted effects of Chr-NE attachments are rationalized by intuitive volume vs. surface accessibility arguments.

Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization

Recent experiments showing scaling of the intrachromosomal contact probability, P(s)∼s(-1) with the genomic distance s, are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of P(s) varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling chromosomes inside a nucleus as a homopolymer confined to a sphere of varying sizes. Brownian dynamics simulations show that the chain dynamics slows down as the polymer volume fraction (ϕ) inside the confinement approaches a critical value ϕ(c). The universal value of ϕ(c)(∞)≈0.44 for a sufficiently long polymer (N≫1) allows us to discuss genome dynamics using ϕ as the sole parameter. Our study shows that the onset of glassy dynamics is the reason for the segregated chromosome organization in humans (N≈3×10(9), ϕ≳ϕ(c)(∞)), whereas chromosomes of budding yeast (N≈10(8), ϕ<ϕ(c)(∞)) are equilibrated with no clear signature of such organization.

Spatial reorganization of telomeres in long-lived quiescent cells

Background

The spatiotemporal behavior of chromatin is an important control mechanism of genomic function. Studies in Saccharomyces cerevisiae have broadly contributed to demonstrate the functional importance of nuclear organization. Although in the wild yeast survival depends on their ability to withstand adverse conditions, most of these studies were conducted on cells undergoing exponential growth. In these conditions, as in most eukaryotic cells, silent chromatin that is mainly found at the 32 telomeres accumulates at the nuclear envelope, forming three to five foci.

Results

Here, combining live microscopy, DNA FISH and chromosome conformation capture (HiC) techniques, we report that chromosomes adopt distinct organizations according to the metabolic status of the cell. In particular, following carbon source exhaustion the genome of long-lived quiescent cells undergoes a major spatial re-organization driven by the grouping of telomeres into a unique focus or hypercluster localized in the center of the nucleus. This change in genome conformation is specific to quiescent cells able to sustain long-term viability. We further show that reactive oxygen species produced by mitochondrial activity during respiration commit the cell to form a hypercluster upon starvation. Importantly, deleting the gene encoding telomere associated silencing factor SIR3 abolishes telomere grouping and decreases longevity, a defect that is rescued by expressing a silencing defective SIR3 allele competent for hypercluster formation.

Conclusions

Our data show that mitochondrial activity primes cells to group their telomeres into a hypercluster upon starvation, reshaping the genome architecture into a conformation that may contribute to maintain longevity of quiescent cells.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-015-0766-2) contains supplementary material, which is available to authorized users.

Analysis methods for studying the 3D architecture of the genome

The rapidly increasing quantity of genome-wide chromosome conformation capture data presents great opportunities and challenges in the computational modeling and interpretation of the three-dimensional genome. In particular, with recent trends towards higher-resolution high-throughput chromosome conformation capture (Hi-C) data, the diversity and complexity of biological hypotheses that can be tested necessitates rigorous computational and statistical methods as well as scalable pipelines to interpret these datasets. Here we review computational tools to interpret Hi-C data, including pipelines for mapping, filtering, and normalization, and methods for confidence estimation, domain calling, visualization, and three-dimensional modeling.

Analysis of Single Locus Trajectories for Extracting In Vivo Chromatin Tethering Interactions

Is it possible to extract tethering forces applied on chromatin from the statistics of a single locus trajectories imaged in vivo? Chromatin fragments interact with many partners such as the nuclear membrane, other chromosomes or nuclear bodies, but the resulting forces cannot be directly measured in vivo. However, they impact chromatin dynamics and should be reflected in particular in the motion of a single locus. We present here a method based on polymer models and statistics of single trajectories to extract the force characteristics and in particular when they are generated by the gradient of a quadratic potential well. Using numerical simulations of a Rouse polymer and live cell imaging of the MAT-locus located on the yeast Saccharomyces cerevisiae chromosome III, we recover the amplitude and the distance between the observed and the interacting monomer. To conclude, the confined trajectories we observed in vivo reflect local interaction on chromatin.

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

Background

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

Results

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

Conclusions

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

Electronic supplementary material

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

Principles of chromatin organization in yeast: relevance of polymer models to describe nuclear organization and dynamics

Nuclear organization can impact on all aspects of the genome life cycle. This organization is thoroughly investigated by advanced imaging and chromosome conformation capture techniques, providing considerable amount of datasets describing the spatial organization of chromosomes. In this review, we will focus on polymer models to describe chromosome statics and dynamics in the yeast Saccharomyces cerevisiae. We suggest that the equilibrium configuration of a polymer chain tethered at both ends and placed in a confined volume is consistent with the current literature, implying that local chromatin interactions play a secondary role in yeast nuclear organization. Future challenges are to reach an integrated multi-scale description of yeast chromosome organization, which is crucially needed to improve our understanding of the regulation of genomic transaction.

Inferential modeling of 3D chromatin structure

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

A simple biophysical model emulates budding yeast chromosome condensation

Mitotic chromosomes were one of the first cell biological structures to be described, yet their molecular architecture remains poorly understood. We have devised a simple biophysical model of a 300 kb-long nucleosome chain, the size of a budding yeast chromosome, constrained by interactions between binding sites of the chromosomal condensin complex, a key component of interphase and mitotic chromosomes. Comparisons of computational and experimental (4C) interaction maps, and other biophysical features, allow us to predict a mode of condensin action. Stochastic condensin-mediated pairwise interactions along the nucleosome chain generate native-like chromosome features and recapitulate chromosome compaction and individualization during mitotic condensation. Higher order interactions between condensin binding sites explain the data less well. Our results suggest that basic assumptions about chromatin behavior go a long way to explain chromosome architecture and are able to generate a molecular model of what the inside of a chromosome is likely to look like.

Topology, structures, and energy landscapes of human chromosomes

Chromosome conformation capture experiments provide a rich set of data concerning the spatial organization of the genome. We use these data along with a maximum entropy approach to derive a least-biased effective energy landscape for the chromosome. Simulations of the ensemble of chromosome conformations based on the resulting information theoretic landscape not only accurately reproduce experimental contact probabilities, but also provide a picture of chromosome dynamics and topology. The topology of the simulated chromosomes is probed by computing the distribution of their knot invariants. The simulated chromosome structures are largely free of knots. Topologically associating domains are shown to be crucial for establishing these knotless structures. The simulated chromosome conformations exhibit a tendency to form fibril-like structures like those observed via light microscopy. The topologically associating domains of the interphase chromosome exhibit multistability with varying liquid crystalline ordering that may allow discrete unfolding events and the landscape is locally funneled toward "ideal" chromosome structures that represent hierarchical fibrils of fibrils.

Comparative 3D genome structure analysis of the fission and the budding yeast

We studied the 3D structural organization of the fission yeast genome, which emerges from the tethering of heterochromatic regions in otherwise randomly configured chromosomes represented as flexible polymer chains in an nuclear environment. This model is sufficient to explain in a statistical manner many experimentally determined distinctive features of the fission yeast genome, including chromatin interaction patterns from Hi-C experiments and the co-locations of functionally related and co-expressed genes, such as genes expressed by Pol-III. Our findings demonstrate that some previously described structure-function correlations can be explained as a consequence of random chromatin collisions driven by a few geometric constraints (mainly due to centromere-SPB and telomere-NE tethering) combined with the specific gene locations in the chromosome sequence. We also performed a comparative analysis between the fission and budding yeast genome structures, for which we previously detected a similar organizing principle. However, due to the different chromosome sizes and numbers, substantial differences are observed in the 3D structural genome organization between the two species, most notably in the nuclear locations of orthologous genes, and the extent of nuclear territories for genes and chromosomes. However, despite those differences, remarkably, functional similarities are maintained, which is evident when comparing spatial clustering of functionally related genes in both yeasts. Functionally related genes show a similar spatial clustering behavior in both yeasts, even though their nuclear locations are largely different between the yeast species.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

Genome sequences provide the overall genetic blueprint of cells, but cells possessing the same genome can exhibit diverse phenotypes. There is a multitude of mechanisms controlling cellular epigenetic states and that dictate the behavior of cells. Among these, networks of interacting molecules, often under stochastic control, depending on the specific wirings of molecular components and the physiological conditions, can have a different landscape of cellular states. In addition, chromosome folding in three-dimensional space provides another important control mechanism for selective activation and repression of gene expression. Fully differentiated cells with different properties grow, divide, and interact through mechanical forces and communicate through signal transduction, resulting in the formation of complex tissue patterns. Developing quantitative models to study these multi-scale phenomena and to identify opportunities for improving human health requires development of theoretical models, algorithms, and computational tools. Here we review recent progress made in these important directions.

Effect of chromosome tethering on nuclear organization in yeast

Interphase chromosomes in Saccharomyces cerevisiae are tethered to the nuclear envelope at their telomeres and to the spindle pole body (SPB) at their centromeres. Using a polymer model of yeast chromosomes that includes these interactions, we show theoretically that telomere attachment to the nuclear envelope is a major determinant of gene positioning within the nucleus only for genes within 10 kb of the telomeres. We test this prediction by measuring the distance between the SPB and the silent mating locus (HML) on chromosome III in wild-type and mutant yeast strains that contain altered chromosome-tethering interactions. In wild-type yeast cells we find that disruption of the telomere tether does not dramatically change the position of HML with respect to the SPB, in agreement with theoretical predictions. Alternatively, using a mutant strain with a synthetic tether that localizes an HML-proximal site to the nuclear envelope, we find a significant change in the SPB-HML distance, again as predicted by theory. Our study quantifies the importance of tethering at telomeres on the organization of interphase chromosomes in yeast, which has been shown to play a significant role in determining chromosome function such as gene expression and recombination.

Investigation of the chromosome regions with significant affinity for the nuclear envelope in fruit fly--a model based approach

Three dimensional nuclear architecture is important for genome function, but is still poorly understood. In particular, little is known about the role of the “boundary conditions” – points of attachment between chromosomes and the nuclear envelope. We describe a method for modeling the 3D organization of the interphase nucleus, and its application to analysis of chromosome-nuclear envelope (Chr-NE) attachments of polytene (giant) chromosomes in Drosophila melanogaster salivary glands. The model represents chromosomes as self-avoiding polymer chains confined within the nucleus; parameters of the model are taken directly from experiment, no fitting parameters are introduced. Methods are developed to objectively quantify chromosome territories and intertwining, which are discussed in the context of corresponding experimental observations. In particular, a mathematically rigorous definition of a territory based on convex hull is proposed. The self-avoiding polymer model is used to re-analyze previous experimental data; the analysis suggests 33 additional Chr-NE attachments in addition to the 15 already explored Chr-NE attachments. Most of these new Chr-NE attachments correspond to intercalary heterochromatin – gene poor, dark staining, late replicating regions of the genome; however, three correspond to euchromatin – gene rich, light staining, early replicating regions of the genome. The analysis also suggests 5 regions of anti-contact, characterized by aversion for the NE, only two of these correspond to euchromatin. This composition of chromatin suggests that heterochromatin may not be necessary or sufficient for the formation of a Chr-NE attachment. To the extent that the proposed model represents reality, the confinement of the polytene chromosomes in a spherical nucleus alone does not favor the positioning of specific chromosome regions at the NE as seen in experiment; consequently, the 15 experimentally known Chr-NE attachment positions do not appear to arise due to non-specific (entropic) forces. Robustness of the key conclusions to model assumptions is thoroughly checked.

Histone variants: the tricksters of the chromatin world

The eukaryotic genome exists in vivo at an equimolar ratio with histones, thus forming a polymer composed of DNA and histone proteins. Each nucleosomal unit in this polymer provides versatile capabilities and dynamic range. Substitutions of the individual components of the histone core with structurally distinct histone variants and covalent modifications alter the local fabric of the chromatin fiber, resulting in epigenetic changes that can be regulated by the cell. In this review, we highlight recent advances in the study of histone variant structure, assembly, and inheritance, their influence on nucleosome positioning, and their cumulative effect upon gene expression, DNA repair and the progression of disease. We also highlight fundamental questions that remain unanswered regarding the behavior of histone variants and their influence on cellular function in the normal and diseased states.

Time scales in epigenetic dynamics and phenotypic heterogeneity of embryonic stem cells

A remarkable feature of the self-renewing population of embryonic stem cells (ESCs) is their phenotypic heterogeneity: Nanog and other marker proteins of ESCs show large cell-to-cell variation in their expression level, which should significantly influence the differentiation process of individual cells. The molecular mechanism and biological implication of this heterogeneity, however, still remain elusive. We address this problem by constructing a model of the core gene-network of mouse ESCs. The model takes account of processes of binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and modification of histone code at each locus of genes in the network. These processes are hierarchically interrelated to each other forming the dynamical feedback loops. By simulating stochastic dynamics of this model, we show that the phenotypic heterogeneity of ESCs can be explained when the chromatin at the Nanog locus undergoes the large scale reorganization in formation/dissolution of transcription apparatus, which should have the timescale similar to the cell cycle period. With this slow transcriptional switching of Nanog, the simulated ESCs fluctuate among multiple transient states, which can trigger the differentiation into the lineage-specific cell states. From the simulated transitions among cell states, the epigenetic landscape underlying transitions is calculated. The slow Nanog switching gives rise to the wide basin of ESC states in the landscape. The bimodal Nanog distribution arising from the kinetic flow running through this ESC basin prevents transdifferentiation and promotes the definite decision of the cell fate. These results show that the distribution of timescales of the regulatory processes is decisively important to characterize the fluctuation of cells and their differentiation process. The analyses through the epigenetic landscape and the kinetic flow on the landscape should provide a guideline to engineer cell differentiation.

Embryonic stem cells (ESCs) can proliferate indefinitely by keeping pluripotency, i.e., the ability to differentiate into any cell-lineage. ESCs, therefore, have been the focus of intense biological and medical interests. A remarkable feature of ESCs is their phenotypic heterogeneity: ESCs show large cell-to-cell fluctuation in the expression level of Nanog, which is a key factor to maintain pluripotency. Since Nanog regulates many genes in ESCs, this fluctuation should seriously affect individual cells when they start differentiation. In this paper we analyze this phenotypic fluctuation by simulating the stochastic dynamics of gene network in ESCs. The model takes account of the mutually interrelated processes of gene regulation such as binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and histone-code modification. We show the distribution of timescales of these processes is decisively important to characterize the dynamical behavior of the gene network, and that the slow formation/dissolution of transcription apparatus at the Nanog locus explains the observed large fluctuation of ESCs. The epigenetic landscapes are calculated based on the stochastic simulation, and the role of the phenotypic fluctuation in the differentiation process is analyzed through the landscape picture.