Large Scale Chromosome Folding Is Stable against Local Changes in Chromatin Structure

Transcription modulates chromatin dynamics and locus configuration sampling

In living cells, the 3D structure of gene loci is dynamic, but this is not revealed by 3C and FISH experiments in fixed samples, leaving a notable gap in our understanding. To overcome these limitations, we applied the highly predictive heteromorphic polymer (HiP-HoP) model to determine chromatin fiber mobility at the Pax6 locus in three mouse cell lines with different transcription states. While transcriptional activity minimally affects movement of 40-kbp regions, we observed that motion of smaller 1-kbp regions depends strongly on local disruption to chromatin fiber structure marked by H3K27 acetylation. This also substantially influenced locus configuration dynamics by modulating protein-mediated promoter-enhancer loops. Importantly, these simulations indicate that chromatin dynamics are sufficiently fast to sample all possible locus conformations within minutes, generating wide dynamic variability within single cells. This combination of simulation and experimental validation provides insight into how transcriptional activity influences chromatin structure and gene dynamics.

Predicting scale-dependent chromatin polymer properties from systematic coarse-graining

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations.

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.

Advances and challenges in CRISPR-based real-time imaging of dynamic genome organization

Nuclear chromosome compaction is non-random and dynamic. The spatial distance among genomic elements instantly modulates transcription. Visualization of the genome organization in the cell nucleus is essential to understand nuclear function. In addition to cell type-dependent organization, high-resolution 3D imaging shows heterogeneous compaction of chromatin organization among the same cell type. Questions remain to be answered if these structural variations were the snapshots of dynamic organization at different time points and if they are functionally different. Live-cell imaging has provided unique insights into dynamic genome organization at short (milliseconds) and long (hours) time scales. The recent development of CRISPR-based imaging opened windows for studying dynamic chromatin organization in single cells in real time. Here we highlight these CRISPR-based imaging techniques and discuss their advances and challenges as a powerful live-cell imaging method that poses high potential to generate paradigm-shifting discoveries and reveal functional implications of dynamic chromatin organization.

Effect of ring stiffness and ambient pressure on the dynamical slowdown in ring polymers

Using extensive molecular dynamics simulations, we investigate the slowdown of dynamics in a 3D system of ring polymers by varying the ambient pressure and the stiffness of the rings. Our study demonstrates that the stiffness of the rings determines the dynamics of the ring polymers, leading to glassiness at lower pressures for stiffer rings. The threading of the ring polymers, a unique feature that emerges only due to the topological nature of such polymers in three dimensions, is shown to be the determinant feature of dynamical slowdown, albeit only in a certain stiffness range. Our results suggest a possible framework for exploring the phase space spanned by ring stiffness and pressure to obtain spontaneously emerging topologically constrained polymer glasses.

Loops, topologically associating domains, compartments, and territories are elastic and robust to dramatic nuclear volume swelling

Layers of genome organization are becoming increasingly better characterized, but less is known about how these structures respond to perturbation or shape changes. Low-salt swelling of isolated chromatin fibers or nuclei has been used for decades to investigate the structural properties of chromatin. But, visible changes in chromatin appearance have not been linked to known building blocks of genome structure or features along the genome sequence. We combine low-salt swelling of isolated nuclei with genome-wide chromosome conformation capture (Hi-C) and imaging approaches to probe the effects of chromatin extension genome-wide. Photoconverted patterns on nuclei during expansion and contraction indicate that global genome structure is preserved after dramatic nuclear volume swelling, suggesting a highly elastic chromosome topology. Hi-C experiments before, during, and after nuclear swelling show changes in average contact probabilities at short length scales, reflecting the extension of the local chromatin fiber. But, surprisingly, during this large increase in nuclear volume, there is a striking maintenance of loops, TADs, active and inactive compartments, and chromosome territories. Subtle differences after expansion are observed, suggesting that the local chromatin state, protein interactions, and location in the nucleus can affect how strongly a given structure is maintained under stress. From these observations, we propose that genome topology is robust to extension of the chromatin fiber and isotropic shape change, and that this elasticity may be beneficial in physiological circumstances of changes in nuclear size and volume.

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

Observation of nucleic acid and protein correlation in chromatin of HeLa nuclei using small-angle neutron scattering with D_{2}O-H_{2}O contrast variation

The small-angle neutron scattering (SANS) on HeLa nuclei demonstrates the bifractal nature of the chromatin structural organization. The border line between two fractal structures is detected as a crossover point at Q_{c}≈4×10^{-2}nm^{-1} in the momentum transfer dependence Q^{-D}. The use of contrast variation (D_{2}O-H_{2}O) in SANS measurements reveals clear similarity in the large scale structural organizations of nucleic acids (NA) and proteins. Both NA and protein structures have a mass fractal arrangement with the fractal dimension of D≈2.5 at scales smaller than 150 nm down to 20 nm. Both NA and proteins show a logarithmic fractal behavior with D≈3 at scales larger than 150 nm up to 6000 nm. The combined analysis of the SANS and atomic force microscopy data allows one to conclude that chromatin and its constitutes (DNA and proteins) are characterized as soft, densely packed, logarithmic fractals on the large scale and as rigid, loosely packed, mass fractals on the smaller scale. The comparison of the partial cross sections from NA and proteins with one from chromatin as a whole demonstrates spatial correlation of two chromatin's components in the range up to 900 nm. Thus chromatin in HeLa nuclei is built as the unified structure of the NA and proteins entwined through each other. Correlation between two components is lost upon scale increases toward 6000 nm. The structural features at the large scale, probably, provide nuclei with the flexibility and chromatin-free space to build supercorrelations on the distance of 10^{3} nm resembling cycle cell activity, such as an appearance of nucleoli and a DNA replication.

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

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

Monitoring the spatio-temporal organization and dynamics of the genome

The spatio-temporal organization of chromatin in the eukaryotic cell nucleus is of vital importance for transcription, DNA replication and genome maintenance. Each of these activities is tightly regulated in both time and space. While we have a good understanding of chromatin organization in space, for example in fixed snapshots as a result of techniques like FISH and Hi-C, little is known about chromatin dynamics in living cells. The rapid development of flexible genomic loci imaging approaches can address fundamental questions on chromatin dynamics in a range of model organisms. Moreover, it is now possible to visualize not only single genomic loci but the whole genome simultaneously. These advances have opened many doors leading to insight into several nuclear processes including transcription and DNA repair. In this review, we discuss new chromatin imaging methods and how they have been applied to study transcription.

Disordered chromatin packing regulates phenotypic plasticity

Three-dimensional supranucleosomal chromatin packing plays a profound role in modulating gene expression by regulating transcription reactions through mechanisms such as gene accessibility, binding affinities, and molecular diffusion. Here, we use a computational model that integrates disordered chromatin packing (CP) with local macromolecular crowding (MC) to study how physical factors, including chromatin density, the scaling of chromatin packing, and the size of chromatin packing domains, influence gene expression. We computationally and experimentally identify a major role of these physical factors, specifically chromatin packing scaling, in regulating phenotypic plasticity, determining responsiveness to external stressors by influencing both intercellular transcriptional malleability and heterogeneity. Applying CPMC model predictions to transcriptional data from cancer patients, we identify an inverse relationship between patient survival and phenotypic plasticity of tumor cells.

Polymer models for the mechanisms of chromatin 3D folding: review and perspective

In this perspective paper, classical physical models for mammalian interphase chromatin folding are reviewed.

Merging 1D and 3D genomic information: Challenges in modelling and validation

Genome organization in eukaryotes during interphase stems from the delicate balance between non-random correlations present in the DNA polynucleotide linear sequence and the physico/chemical reactions which shape continuously the form and structure of DNA and chromatin inside the nucleus of the cell. It is now clear that these mechanisms have a key role in important processes like gene regulation, yet the detailed ways they act simultaneously and, eventually, come to influence each other even across very different length-scales remain largely unexplored. In this paper, we recapitulate some of the main results concerning gene regulatory and physical mechanisms, in relation to the information encoded in the 1D sequence and the 3D folding structure of DNA. In particular, we stress how reciprocal crossfeeding between 1D and 3D models may provide original insight into how these complex processes work and influence each other. This article is part of a Special Issue entitled: Transcriptional Profiles and Regulatory Gene Networks edited by Dr. Dr. Federico Manuel Giorgi and Dr. Shaun Mahony.

Microrheology of interphase chromosomes with spatial constraints: a computational study

Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton, an ensemble of 'extra-chromatin' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell, their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue, in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-versus-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales, we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems, namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.

Polymer Simulations of Heteromorphic Chromatin Predict the 3D Folding of Complex Genomic Loci

Chromatin folded into 3D macromolecular structures is often analyzed by chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) techniques, but these frequently provide contradictory results. Chromatin can be modeled as a simple polymer composed of a connected chain of units. By embedding data for epigenetic marks (H3K27ac), chromatin accessibility (assay for transposase-accessible chromatin using sequencing [ATAC-seq]), and structural anchors (CCCTC-binding factor [CTCF]), we developed a highly predictive heteromorphic polymer (HiP-HoP) model, where the chromatin fiber varied along its length; combined with diffusing protein bridges and loop extrusion, this model predicted the 3D organization of genomic loci at a population and single-cell level. The model was validated at several gene loci, including the complex Pax6 gene, and was able to determine locus conformations across cell types with varying levels of transcriptional activity and explain different mechanisms of enhancer use. Minimal a priori knowledge of epigenetic marks is sufficient to recapitulate complex genomic loci in 3D and enable predictions of chromatin folding paths.

•

HiP-HoP: highly predictive heteromorphic polymer model to analyze chromatin structure

•

Polymer simulations use widely available epigenetic and protein binding data as input

•

Validate HiP-HoP model at complex loci using 3D FISH and Capture-C

•

Simulations uncover striking conformational variability in chromatin fiber folding

Reorganization of inter-chromosomal interactions in the 2q37-deletion syndrome

Chromosomes occupy distinct interphase territories in the three-dimensional nucleus. However, how these chromosome territories are arranged relative to one another is poorly understood. Here, we investigated the inter-chromosomal interactions between chromosomes 2q, 12, and 17 in human mesenchymal stem cells (MSCs) and MSC-derived cell types by DNA-FISH We compared our findings in normal karyotypes with a three-generation family harboring a 2q37-deletion syndrome, featuring a heterozygous partial deletion of histone deacetylase 4 (HDAC4) on chr2q37. In normal karyotypes, we detected stable, recurring arrangements and interactions between the three chromosomal territories with a tissue-specific interaction bias at certain loci. These inter-chromosomal interactions were confirmed by Hi-C. Interestingly, the disease-related HDAC4 deletion resulted in displaced inter-chromosomal arrangements and altered interactions between the deletion-affected chromosome 2 and chromosome 12 and/or 17 in 2q37-deletion syndrome patients. Our findings provide evidence for a direct link between a structural chromosomal aberration and altered interphase architecture that results in a nuclear configuration, supporting a possible molecular pathogenesis.

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

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