Exploring the conformational space of chromatin fibers and their stability by numerical dynamic phase diagrams

Multiscale modeling reveals the ion-mediated phase separation of nucleosome core particles

Due to the vast length scale inside the cell nucleus, multiscale models are required to understand chromatin folding, structure, and dynamics and how they regulate genomic activities such as DNA transcription, replication, and repair. We study the interactions and structure of condensed phases formed by the universal building block of chromatin, the nucleosome core particle (NCP), using bottom-up multiscale coarse-grained (CG) simulations with a model extracted from all-atom MD simulations. In the presence of the multivalent cations Mg(H2O)62+ or CoHex3+, we analyze the internal structures of the NCP aggregates and the contributions of histone tails and ions to the aggregation patterns. We then derive a "super" coarse-grained (SCG) NCP model to study the macroscopic scale phase separation of NCPs. The SCG simulations show the formation of NCP aggregates with Mg(H2O)62+ concentration-dependent densities and sizes. Variation of the CoHex3+ concentrations results in highly ordered lamellocolumnar and hexagonal columnar phases in agreement with experimental data. The results give detailed insights into nucleosome interactions and for understanding chromatin folding in the cell nucleus.

Nucleosome spacing controls chromatin spatial structure and accessibility

Recent research highlights the significance of the three-dimensional structure of chromatin in regulating various cellular processes, particularly transcription. This is achieved through dynamic chromatin structures that facilitate long-range contacts and control spatial accessibility. Chromatin consists of DNA and a variety of proteins, of which histones play an essential structural role by forming nucleosomes. Extensive experimental and theoretical research in recent decades has yielded conflicting results about key factors that regulate the spatial structure of chromatin, which remains enigmatic. By using a computer model that allows us to simulate chromatin volumes containing physiological nucleosome concentrations, we investigated whether nucleosome spacing or nucleosome density is fundamental for three-dimensional chromatin accessibility. Unexpectedly, the regularity of the nucleosome spacing is crucial for determining the accessibility of the chromatin network to diffusive processes, whereas variation in nucleosome concentrations has only minor effects. Using only the basic physical properties of DNA and nucleosomes was sufficient to generate chromatin structures consistent with published electron microscopy data. Contrary to other work, we found that nucleosome density did not substantially alter the properties of chromatin fibers or contact probabilities of genomic loci. No breakup of fiber-like structures was observed at high molar density. These findings challenge previous assumptions and highlight the importance of nucleosome spacing as a key driver of chromatin organization. These results identified changes in nucleosome spacing as a tentative mechanism for altering the spatial chromatin structure and thus genomic functions.

An associative memory Hamiltonian model for DNA and nucleosomes

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), reproduces the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similar to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM is designed to emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, is ready to be scaled up to molecular systems large enough to investigate the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use.

Cohesin and CTCF complexes mediate contacts in chromatin loops depending on nucleosome positions

The spatial organization of the eukaryotic genome plays an important role in regulating transcriptional activity. In the nucleus, chromatin forms loops that assemble into fundamental units called topologically associating domains that facilitate or inhibit long-range contacts. These loops are formed and held together by the ring-shaped cohesin protein complex, and this can involve binding of CCCTC-binding factor (CTCF). High-resolution conformation capture experiments provide the frequency at which two DNA fragments physically associate in three-dimensional space. However, technical limitations of this approach, such as low throughput, low resolution, or noise in contact maps, make data interpretation and identification of chromatin intraloop contacts, e.g., between distal regulatory elements and their target genes, challenging. Herein, an existing coarse-grained model of chromatin at single-nucleosome resolution was extended by integrating potentials describing CTCF and cohesin. We performed replica-exchange Monte Carlo simulations with regularly spaced nucleosomes and experimentally determined nucleosome positions in the presence of cohesin-CTCF, as well as depleted systems as controls. In fully extruded loops caused by the presence of cohesin and CTCF, the number of contacts within the formed loops was increased. The number and types of these contacts were impacted by the nucleosome distribution and loop size. Microloops were observed within cohesin-mediated loops due to thermal fluctuations without additional influence of other factors, and the number, size, and shape of microloops were determined by nucleosome distribution and loop size. Nucleosome positions directly affect the spatial structure and contact probability within a loop, with presumed consequences for transcriptional activity.

Differences in nanoscale organization of regulatory active and inactive human chromatin

Methodological advances in conformation capture techniques have fundamentally changed our understanding of chromatin architecture. However, the nanoscale organization of chromatin and its cell-to-cell variance are less studied. Analyzing genome-wide data from 733 human cell and tissue samples, we identified 2 prototypical regions that exhibit high or absent hypersensitivity to deoxyribonuclease I, respectively. These regulatory active or inactive regions were examined in the lymphoblast cell line K562 by using high-throughput super-resolution microscopy. In both regions, we systematically measured the physical distance of 2 fluorescence in situ hybridization spots spaced by only 5 kb of DNA. Unexpectedly, the resulting distance distributions range from very compact to almost elongated configurations of more than 200-nm length for both the active and inactive regions. Monte Carlo simulations of a coarse-grained model of these chromatin regions based on published data of nucleosome occupancy in K562 cells were performed to understand the underlying mechanisms. There was no parameter set for the simulation model that can explain the microscopically measured distance distributions. Obviously, the chromatin state given by the strength of internucleosomal interaction, nucleosome occupancy, or amount of histone H1 differs from cell to cell, which results in the observed broad distance distributions. This large variability was not expected, especially in inactive regions. The results for the mechanisms for different distance distributions on this scale are important for understanding the contacts that mediate gene regulation. Microscopic measurements show that the inactive region investigated here is expected to be embedded in a more compact chromatin environment. The simulation results of this region require an increase in the strength of internucleosomal interactions. It may be speculated that the higher density of chromatin is caused by the increased internucleosomal interaction strength.

How Genomes Emerge, Function, and Evolve: Living Systems Emergence-Genotype-Phenotype-Multilism-Genome/Systems Ecology

What holds together the world in its innermost, what life is, how it emerges, functions, and evolves, has not only been an epic matter of endless romantic sunset poetry and philosophy, but also manifests explicitly in its perhaps most central organization unit-genomes. Their 3D architecture and dynamics, including the interaction networks of regulatory elements, obviously co-evolved as inseparable systems allowing the physical storage, expression, and replication of genetic information. Since we were able to fill finally the much-debated centennial gaps in their 3D architecture and dynamics, now entire new perspectives open beyond epigenetics reaching as far as a general understanding of living systems: besides the previously known DNA double helix and nucleosome structure, the latter compact into a chromatin quasi-fibre folded into stable loops forming stable multi-loop aggregates/rosettes connected by linkers, creating hence the again already known chromosome arms and entire chromosomes forming the cell nucleus. Instantly and for the first time this leads now to a consistent and cross-proven systems statistical mechanics genomics framework elucidating genome intrinsic function and regulation including various components. It balances stability/flexibility ensuring genome integrity, enabling expression/regulation of genetic information, as well as genome replication/spread. Furthermore, genotype and phenotype are multiplisticly entangled being evolutionarily the outcome of both Darwinian natural selection and Lamarckian self-referenced manipulation-all embedded in even broader genome ecology (autopoietic) i(!)n- and environmental scopes. This allows formulating new meta-level functional semantics of genomics, i.e. notions as communication of genes, genomes, and information networks, architectural and dynamic spaces for creativity and innovation, or genomes as central geno-/phenotype entanglements. Beyond and most fundamentally, the paradoxical-seeming local equilibrium substance stability in its entity though far from a universal heat-death-like equilibrium is solved, and system irreversibility, time directionality, and thus the emergence of existence are clarified. Consequently, real deep understandings of genomes, life, and complex systems in general appear in evolutionary perspectives as well as from systems analyses, via system damage/disease (its repair/cure and manipulation) as far as the understanding of extraterrestrial life, the de novo creation and thus artificial life, and even the raison d'etre.

Simulation of Different Three-Dimensional Models of Whole Interphase Nuclei Compared to Experiments - A Consistent Scale-Bridging Simulation Framework for Genome Organization

The three-dimensional architecture of chromosomes, their arrangement, and dynamics within cell nuclei are still subject of debate. Obviously, the function of genomes-the storage, replication, and transcription of genetic information-has closely coevolved with this architecture and its dynamics, and hence are closely connected. In this work a scale-bridging framework investigates how of the 30 nm chromatin fibre organizes into chromosomes including their arrangement and morphology in the simulation of whole nuclei. Therefore, mainly two different topologies were simulated with corresponding parameter variations and comparing them to experiments: The Multi-Loop-Subcompartment (MLS) model, in which (stable) small loops form (stable) rosettes, connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop and linker sizes. The 30 nm chromatin fibre was modelled as a polymer chain with stretching, bending and excluded volume interactions. A spherical boundary potential simulated the confinement to nuclei with different radii. Simulated annealing and Brownian Dynamics methods were applied in a four-step decondensation procedure to generate from metaphase decondensated interphase configurations at thermodynamical equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes result in distinct subchromosomal domains visible in electron and confocal laser scanning microscopic images. In contrast, the big RW/GL loops lead to a mostly homogeneous chromatin distribution. Even small changes of the model parameters induced significant rearrangements of the chromatin morphology. The low overlap of chromosomes, arms, and subchromosomal domains observed in experiments agrees only with the MLS model. The chromatin density distribution in CLSM image stacks reveals a bimodal behaviour in agreement with recent experiments. Combination of these results with a variety of (spatial distance) measurements favour an MLS like model with loops and linkers of 63 to 126 kbp. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and is in disagreement with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist and are necessary for transport. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the diffusion of molecules, and other measurements. Also all other chromosome topologies can in principle be excluded. In summary, polymer simulations of whole nuclei compared to experimental data not only clearly favour only a stable loop aggregate/rosette like genome architecture whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus and hence can be used for understanding genome organization also in respect to diagnosis and treatment. This is in agreement with and also leads to a general novel framework of genome emergence, function, and evolution.

Soft-matter properties of multilayer chromosomes

This perspective aims to identify the relationships between the structural and dynamic properties of chromosomes and the fundamental properties of soft-matter systems. Chromatin is condensed into metaphase chromosomes during mitosis. The resulting structures are elongated cylinders having micrometer-scale dimensions. Our previous studies, using transmission electron microscopy, atomic force microscopy, and cryo-electron tomography, suggested that metaphase chromosomes have a multilayered structure, in which each individual layer has the width corresponding to a mononucleosome sheet. The self-assembly of multilayer chromatin plates from small chromatin fragments suggests that metaphase chromosomes are self-organized hydrogels (in which a single DNA molecule crosslinks the whole structure) with an internal liquid-crystal order produced by the stacking of chromatin layers along the chromosome axis. This organization of chromatin was unexpected, but the spontaneous assembly of large structures has been studied in different soft-matter systems and, according to these studies, the self-organization of chromosomes could be justified by the interplay between weak interactions of repetitive nucleosome building blocks and thermal fluctuations. The low energy of interaction between relatively large building blocks also justifies the easy deformation and structural fluctuations of soft-matter structures and the changes of phase caused by diverse external factors. Consistent with these properties of soft matter, different experimental results show that metaphase chromosomes are easily deformable. Furthermore, at the end of mitosis, condensed chromosomes undergo a phase transition into a more fluid structure, which can be correlated to the decrease in the Mg²⁺concentration and to the dissociation of condensins from chromosomes. Presumably, the unstacking of layers and chromatin fluctuations driven by thermal energy facilitate gene expression during interphase.

Nucleosome plasticity is a critical element of chromatin liquid-liquid phase separation and multivalent nucleosome interactions

Liquid-liquid phase separation (LLPS) is an important mechanism that helps explain the membraneless compartmentalization of the nucleus. Because chromatin compaction and LLPS are collective phenomena, linking their modulation to the physicochemical features of nucleosomes is challenging. Here, we develop an advanced multiscale chromatin model-integrating atomistic representations, a chemically-specific coarse-grained model, and a minimal model-to resolve individual nucleosomes within sub-Mb chromatin domains and phase-separated systems. To overcome the difficulty of sampling chromatin at high resolution, we devise a transferable enhanced-sampling Debye-length replica-exchange molecular dynamics approach. We find that nucleosome thermal fluctuations become significant at physiological salt concentrations and destabilize the 30-nm fiber. Our simulations show that nucleosome breathing favors stochastic folding of chromatin and promotes LLPS by simultaneously boosting the transient nature and heterogeneity of nucleosome-nucleosome contacts, and the effective nucleosome valency. Our work puts forward the intrinsic plasticity of nucleosomes as a key element in the liquid-like behavior of nucleosomes within chromatin, and the regulation of chromatin LLPS.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

1CPN: A coarse-grained multi-scale model of chromatin

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

Biophysics of Chromatin Dynamics

Nucleosomes and chromatin control eukaryotic genome accessibility and thereby regulate DNA processes, including transcription, replication, and repair. Conformational dynamics within the nucleosome and chromatin structure play a key role in this regulatory function. Structural fluctuations continuously expose internal DNA sequences and nucleosome surfaces, thereby providing transient access for the nuclear machinery. Progress in structural studies of nucleosomes and chromatin has provided detailed insight into local chromatin organization and has set the stage for recent in-depth investigations of the structural dynamics of nucleosomes and chromatin fibers. Here, we discuss the dynamic processes observed in chromatin over different length scales and timescales and review current knowledge about the biophysics of distinct structural transitions.

Frozen-hydrated chromatin from metaphase chromosomes has an interdigitated multilayer structure

Cryo-electron tomography and small-angle X-ray scattering were used to investigate the chromatin folding in metaphase chromosomes. The tomographic 3D reconstructions show that frozen-hydrated chromatin emanated from chromosomes is planar and forms multilayered plates. The layer thickness was measured accounting for the contrast transfer function fringes at the plate edges, yielding a width of ~ 7.5 nm, which is compatible with the dimensions of a monolayer of nucleosomes slightly tilted with respect to the layer surface. Individual nucleosomes are visible decorating distorted plates, but typical plates are very dense and nucleosomes are not identifiable as individual units, indicating that they are tightly packed. Two layers in contact are ~ 13 nm thick, which is thinner than the sum of two independent layers, suggesting that nucleosomes in the layers interdigitate. X-ray scattering of whole chromosomes shows a main scattering peak at ~ 6 nm, which can be correlated with the distance between layers and between interdigitating nucleosomes interacting through their faces. These observations support a model where compact chromosomes are composed of many chromatin layers stacked along the chromosome axis.

A Guided Protocol for Array Based T2C: A High-Quality Selective High-Resolution High-Throughput Chromosome Interaction Capture

After now more than 170 years of research the dynamic three-dimensional chromatin architecture of genomes and the co-evolved interaction networks of regulatory elements which create genome function - i.e. the storage, expression, and finally replication of genetic information - involves ever more investigative efforts in respect to not only the pure understanding of living organisms, but also diagnosis, treatment, and even future genome engineering. To study genomic interactions, we developed a novel and superior high-quality selective high-resolution, high-throughput chromosome interaction capture method - T2C (targeted chromatin capture) - which allows to arbitrarily balance resolution, frequency range of interactions, and the investigated general genetic region or single interactions in a highly cost-effective manner in respect to the obtainable result and compared to other techniques. Beyond, T2C has such a high signal-to-noise ratio at high resolution that the "genomic" statistical mechanics level can be reached. With the guided T2C protocol described here, we were already able to finally determine the chromatin quasi-fiber conformation and its folding into stable multi-loop aggregates/rosettes connected by a linker. Actually, this guided T2C protocol provides the means for architectural genome sequencing from the level of the single base pair to the entire cell nucleus and thus to analyze genetic interactions in respect to genome function in a systems biological manner in general as well as in settings ranging from basic research, via diagnostics and treatment, to genome engineering. © 2018 by John Wiley & Sons, Inc.

Simulation of different three-dimensional polymer models of interphase chromosomes compared to experiments-an evaluation and review framework of the 3D genome organization

Despite all the efforts the three-dimensional higher-order architecture and dynamics in the cell nucleus are still debated. The regulation of genes, their transcription, replication, as well as differentiation in Eukarya is, however, closely connected to this architecture and dynamics. Here, an evaluation and review framework is setup to investigate the folding of a 30 nm chromatin fibre into chromosome territories by comparing computer simulations of two different chromatin topologies to experiments: The Multi-Loop-Subcompartment (MLS) model, in which small loops form rosettes connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop, rosette, and linker sizes. The 30 nm chromatin fibre was modelled as a polymer chain with stretching, bending, and excluded volume interactions. A spherical boundary potential simulated the confinement by other chromosomes and the nuclear envelope. Monte Carlo and Brownian Dynamics methods were applied to generate chain configurations at thermodynamic equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes form distinct subchromosomal domains, compatible in size as those from light microscopic observations. In contrast, the big RW/GL loops lead to a more homogeneous chromatin distribution. Only the MLS model agrees with the low overlap of chromosomes, their arms, and subchromosomal domains found experimentally. A review of experimental spatial distance measurements between genomic markers labelled by FISH as a function of their genomic separation from different publications and comparison to simulated spatial distances also favours an MLS-like model with loops and linkers of 63 to 126 kbp. The chromatin folding topology also reduces the apparent persistence length of the chromatin fibre to a value significantly lower than the free solution persistence length, explaining the low persistence lengths found various experiments. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and disagrees with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the nuclear diffusion of molecules, as well as other experiments. In summary, this polymer simulation framework compared to experimental data clearly favours only a quasi-chromatin fibre forming a stable multi-loop aggregate/rosette like genome organization and dynamics whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus.

The detailed 3D multi-loop aggregate/rosette chromatin architecture and functional dynamic organization of the human and mouse genomes

BACKGROUND

The dynamic three-dimensional chromatin architecture of genomes and its co-evolutionary connection to its function-the storage, expression, and replication of genetic information-is still one of the central issues in biology. Here, we describe the much debated 3D architecture of the human and mouse genomes from the nucleosomal to the megabase pair level by a novel approach combining selective high-throughput high-resolution chromosomal interaction capture (T2C), polymer simulations, and scaling analysis of the 3D architecture and the DNA sequence.

RESULTS

The genome is compacted into a chromatin quasi-fibre with ~5 ± 1 nucleosomes/11 nm, folded into stable ~30-100 kbp loops forming stable loop aggregates/rosettes connected by similar sized linkers. Minor but significant variations in the architecture are seen between cell types and functional states. The architecture and the DNA sequence show very similar fine-structured multi-scaling behaviour confirming their co-evolution and the above.

CONCLUSIONS

This architecture, its dynamics, and accessibility, balance stability and flexibility ensuring genome integrity and variation enabling gene expression/regulation by self-organization of (in)active units already in proximity. Our results agree with the heuristics of the field and allow "architectural sequencing" at a genome mechanics level to understand the inseparable systems genomic properties.

Dynamic properties of independent chromatin domains measured by correlation spectroscopy in living cells

Background

Genome organization into subchromosomal topologically associating domains (TADs) is linked to cell-type-specific gene expression programs. However, dynamic properties of such domains remain elusive, and it is unclear how domain plasticity modulates genomic accessibility for soluble factors.

Results

Here, we combine and compare a high-resolution topology analysis of interacting chromatin loci with fluorescence correlation spectroscopy measurements of domain dynamics in single living cells. We identify topologically and dynamically independent chromatin domains of ~1 Mb in size that are best described by a loop-cluster polymer model. Hydrodynamic relaxation times and gyration radii of domains are larger for open (161 ± 15 ms, 297 ± 9 nm) than for dense chromatin (88 ± 7 ms, 243 ± 6 nm) and increase globally upon chromatin hyperacetylation or ATP depletion.

Conclusions

Based on the domain structure and dynamics measurements, we propose a loop-cluster model for chromatin domains. It suggests that the regulation of chromatin accessibility for soluble factors displays a significantly stronger dependence on factor concentration than search processes within a static network.

Electronic supplementary material

The online version of this article (doi:10.1186/s13072-016-0093-1) contains supplementary material, which is available to authorized users.

Changing chromatin fiber conformation by nucleosome repositioning

Chromatin conformation is dynamic and heterogeneous with respect to nucleosome positions, which can be changed by chromatin remodeling complexes in the cell. These molecular machines hydrolyze ATP to translocate or evict nucleosomes, and establish loci with regularly and more irregularly spaced nucleosomes as well as nucleosome-depleted regions. The impact of nucleosome repositioning on the three-dimensional chromatin structure is only poorly understood. Here, we address this issue by using a coarse-grained computer model of arrays of 101 nucleosomes considering several chromatin fiber models with and without linker histones, respectively. We investigated the folding of the chain in dependence of the position of the central nucleosome by changing the length of the adjacent linker DNA in basepair steps. We found in our simulations that these translocations had a strong effect on the shape and properties of chromatin fibers: i), Fiber curvature and flexibility at the center were largely increased and long-range contacts between distant nucleosomes on the chain were promoted. ii), The highest destabilization of the fiber conformation occurred for a nucleosome shifted by two basepairs from regular spacing, whereas effects of linker DNA changes of ?10 bp in phase with the helical twist of DNA were minimal. iii), A fiber conformation can stabilize a regular spacing of nucleosomes inasmuch as favorable stacking interactions between nucleosomes are facilitated. This can oppose nucleosome translocations and increase the energetic costs for chromatin remodeling. Our computational modeling framework makes it possible to describe the conformational heterogeneity of chromatin in terms of nucleosome positions, and thus advances theoretical models toward a better understanding of how genome compaction and access are regulated within the cell.

The chromatin fiber: multiscale problems and approaches

The structure of chromatin, affected by many factors from DNA linker lengths to posttranslational modifications, is crucial to the regulation of eukaryotic cells. Combined experimental and computational methods have led to new insights into its structural and dynamical features, from interactions due to the flexible core histone tails or linker histones to the physical mechanism driving the formation of chromosomal domains. Here we present a perspective of recent advances in chromatin modeling techniques at the atomic, mesoscopic, and chromosomal scales with a view toward developing multiscale computational strategies to integrate such findings. Innovative modeling methods that connect molecular to chromosomal scales are crucial for interpreting experiments and eventually deciphering the complex dynamic organization and function of chromatin in the cell.

The energy components of stacked chromatin layers explain the morphology, dimensions and mechanical properties of metaphase chromosomes

The measurement of the dimensions of metaphase chromosomes in different animal and plant karyotypes prepared in different laboratories indicates that chromatids have a great variety of sizes which are dependent on the amount of DNA that they contain. However, all chromatids are elongated cylinders that have relatively similar shape proportions (length to diameter ratio approx. 13). To explain this geometry, it is considered that chromosomes are self-organizing structures formed by stacked layers of planar chromatin and that the energy of nucleosome-nucleosome interactions between chromatin layers inside the chromatid is approximately 3.6 × 10(-20) J per nucleosome, which is the value reported by other authors for internucleosome interactions in chromatin fibres. Nucleosomes in the periphery of the chromatid are in contact with the medium; they cannot fully interact with bulk chromatin within layers and this generates a surface potential that destabilizes the structure. Chromatids are smooth cylinders because this morphology has a lower surface energy than structures having irregular surfaces. The elongated shape of chromatids can be explained if the destabilizing surface potential is higher in the telomeres (approx. 0.16 mJ m(-2)) than in the lateral surface (approx. 0.012 mJ m(-2)). The results obtained by other authors in experimental studies of chromosome mechanics have been used to test the proposed supramolecular structure. It is demonstrated quantitatively that internucleosome interactions between chromatin layers can justify the work required for elastic chromosome stretching (approx. 0.1 pJ for large chromosomes). The high amount of work (up to approx. 10 pJ) required for large chromosome extensions is probably absorbed by chromatin layers through a mechanism involving nucleosome unwrapping.

An advanced coarse-grained nucleosome core particle model for computer simulations of nucleosome-nucleosome interactions under varying ionic conditions

In the eukaryotic cell nucleus, DNA exists as chromatin, a compact but dynamic complex with histone proteins. The first level of DNA organization is the linear array of nucleosome core particles (NCPs). The NCP is a well-defined complex of 147 bp DNA with an octamer of histones. Interactions between NCPs are of paramount importance for higher levels of chromatin compaction. The polyelectrolyte nature of the NCP implies that nucleosome-nucleosome interactions must exhibit a great influence from both the ionic environment as well as the positively charged and highly flexible N-terminal histone tails, protruding out from the NCP. The large size of the system precludes a modelling analysis of chromatin at an all-atom level and calls for coarse-grained approximations. Here, a model of the NCP that include the globular histone core and the flexible histone tails described by one particle per each amino acid and taking into account their net charge is proposed. DNA wrapped around the histone core was approximated at the level of two base pairs represented by one bead (bases and sugar) plus four beads of charged phosphate groups. Computer simulations, using a Langevin thermostat, in a dielectric continuum with explicit monovalent (K(+)), divalent (Mg(2+)) or trivalent (Co(NH(3))(6) (3+)) cations were performed for systems with one or ten NCPs. Increase of the counterion charge results in a switch from repulsive NCP-NCP interaction in the presence of K(+), to partial aggregation with Mg(2+) and to strong mutual attraction of all 10 NCPs in the presence of CoHex(3+). The new model reproduced experimental results and the structure of the NCP-NCP contacts is in agreement with available data. Cation screening, ion-ion correlations and tail bridging contribute to the NCP-NCP attraction and the new NCP model accounts for these interactions.

Unwinding and rewinding the nucleosome inner turn: force dependence of the kinetic rate constants

A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.

Nucleosome spacing and chromatin higher-order folding

Packing of about two meters of the human genome DNA into chromatin occupying a several micron-sized cell nucleus requires a high degree of compaction in a manner that allows the information encoded on DNA to remain easily accessible. This packing is mediated by repeated coiling of DNA double helix around histones to form nucleosome arrays that are further folded into higher-order structures. Relatively straight DNA linkers separate the nucleosomes and the spacing between consecutive nucleosome varies between different cells and between different chromosomal loci. In a recent work¹ our group used a biochemically defined in vitro reconstituted system to explore how do various DNA linkers mediate nucleosome array packing into higher-order chromatin structures. For long nucleosome linkers (about 60 bp) we observed a more open chromatin structure and no effect of small linker length alterations (±2−4 bp) on chromatin folding. In striking contrast, for shorter linkers (20−32 bp) we found more compact packing with strong periodical dependence upon the linker DNA lengths. Our data together with high-resolution nucleosome position mapping provide evidence for the natural nucleosome repeats to support a chromatin architecture that, by default, restricts spontaneous folding of nucleosome arrays into compact chromatin fibers. We suggest that incomplete folding of the nucleosome arrays may promote global inter-array interactions that lead to chromatin condensation in metaphase chromosomes and heterochromatin.

Short nucleosome repeats impose rotational modulations on chromatin fibre folding

In eukaryotic cells, DNA is organized into arrays of repeated nucleosomes where the shorter nucleosome repeat length (NRL) types are associated with transcriptionally active chromatin. Here, we tested a hypothesis that systematic variations in the NRL influence nucleosome array folding into higher-order structures. For NRLs with fixed rotational settings, we observed a negative correlation between NRL and chromatin folding. Rotational variations within a range of longer NRLs (188 bp and above) typical of repressed chromatin in differentiated cells did not reveal any changes in chromatin folding. In sharp contrast, for the shorter NRL range of 165-177 bp, we observed a strong periodic dependence of chromatin folding upon the changes in linker DNA lengths, with the 172 bp repeat found in highly transcribed yeast chromatin imposing an unfolded state of the chromatin fibre that could be reversed by linker histone. Our results suggest that the NRL may direct chromatin higher-order structure into either a nucleosome position-dependent folding for short NRLs typical of transcribed genes or an architectural factor-dependent folding typical of longer NRLs prevailing in eukaryotic heterochromatin.

Modelling chromatin structure and dynamics: status and prospects

The packaging of genomic DNA into chromatin in the eukaryotic cell nucleus demands extensive compaction. This requires attractive nucleosome-nucleosome interactions to overcome repulsion between the negatively charged DNA segments as well as other constraints. At the same time, DNA must be dynamically accessible to the cellular machinery that operates on it. Recent progress in the experimental characterisation of the higher order structure and dynamics of well-defined chromatin fibres has stimulated the attempts at theoretical description of chromatin and the nucleosome. Here we review the present status of chromatin modelling, with particular emphasis on coarse-grained computer simulation models, the role of electrostatic interactions, and discuss future perspectives in the field.

Toward convergence of experimental studies and theoretical modeling of the chromatin fiber

Understanding the structural organization of eukaryotic chromatin and its control of gene expression represents one of the most fundamental and open challenges in modern biology. Recent experimental advances have revealed important characteristics of chromatin in response to changes in external conditions and histone composition, such as the conformational complexity of linker DNA and histone tail domains upon compact folding of the fiber. In addition, modeling studies based on high-resolution nucleosome models have helped explain the conformational features of chromatin structural elements and their interactions in terms of chromatin fiber models. This minireview discusses recent progress and evidence supporting structural heterogeneity in chromatin fibers, reconciling apparently contradictory fiber models.

Electron microscopy and atomic force microscopy studies of chromatin and metaphase chromosome structure

The folding of the chromatin filament and, in particular, the organization of genomic DNA within metaphase chromosomes has attracted the interest of many laboratories during the last five decades. This review discusses our current understanding of chromatin higher-order structure based on results obtained with transmission electron microscopy (TEM), cryo-electron microscopy (cryo-EM), and different atomic force microscopy (AFM) techniques. Chromatin isolated from different cell types in buffers without cations form extended filaments with nucleosomes visible as separated units. In presence of low concentrations of Mg(2+), chromatin filaments are folded into fibers having a diameter of ∼ 30 nm. Highly compact fibers were obtained with isolated chromatin fragments in solutions containing 1-2mM Mg(2+). The high density of these fibers suggested that the successive turns of the chromatin filament are interdigitated. Similar results were obtained with reconstituted nucleosome arrays under the same ionic conditions. This led to the proposal of compact interdigitated solenoid models having a helical pitch of 4-5 nm. These findings, together with the observation of columns of stacked nucleosomes in different liquid crystal phases formed by aggregation of nucleosome core particles at high concentration, and different experimental evidences obtained using other approaches, indicate that face-to-face interactions between nucleosomes are very important for the formation of dense chromatin structures. Chromatin fibers were observed in metaphase chromosome preparations in deionized water and in buffers containing EDTA, but chromosomes in presence of the Mg(2+) concentrations found in metaphase (5-22 mM) are very compact, without visible fibers. Moreover, a recent cryo-electron microscopy analysis of vitreous sections of mitotic cells indicated that chromatin has a disordered organization, which does not support the existence of 30-nm fibers in condensed chromosomes. TEM images of partially denatured chromosomes obtained using different procedures that maintain the ionic conditions of metaphase showed that bulk chromatin in chromosomes is organized forming multilayered plate-like structures. The structure and mechanical properties of these plates were studied using cryo-EM, electron tomography, AFM imaging in aqueous media, and AFM-based nanotribology and force spectroscopy. The results obtained indicated that the chromatin filament forms a flexible two-dimensional network, in which DNA is the main component responsible for the mechanical strength observed in friction force measurements. The discovery of this unexpected structure based on a planar geometry has opened completely new possibilities for the understanding of chromatin folding in metaphase chromosomes. It was proposed that chromatids are formed by many stacked thin chromatin plates oriented perpendicular to the chromatid axis. Different experimental evidences indicated that nucleosomes in the plates are irregularly oriented, and that the successive layers are interdigitated (the apparent layer thickness is 5-6 nm), allowing face-to-face interactions between nucleosomes of adjacent layers. The high density of this structure is in agreement with the high concentration of DNA observed in metaphase chromosomes of different species, and the irregular orientation of nucleosomes within the plates make these results compatible with those obtained with mitotic cell cryo-sections. The multilaminar chromatin structure proposed for chromosomes allows an easy explanation of chromosome banding and of the band splitting observed in stretched chromosomes.

Nanotribology results show that DNA forms a mechanically resistant 2D network in metaphase chromatin plates

In a previous study, we found that metaphase chromosomes are formed by thin plates, and here we have applied atomic force microscopy (AFM) and friction force measurements at the nanoscale (nanotribology) to analyze the properties of these planar structures in aqueous media at room temperature. Our results show that high concentrations of NaCl and EDTA and extensive digestion with protease and nuclease enzymes cause plate denaturation. Nanotribology studies show that native plates under structuring conditions (5 mM Mg2+) have a relatively high friction coefficient (μ≈0.3), which is markedly reduced when high concentrations of NaCl or EDTA are added (μ≈0.1). This lubricant effect can be interpreted considering the electrostatic repulsion between DNA phosphate groups and the AFM tip. Protease digestion increases the friction coefficient (μ≈0.5), but the highest friction is observed when DNA is cleaved by micrococcal nuclease (μ≈0.9), indicating that DNA is the main structural element of plates. Whereas nuclease-digested plates are irreversibly damaged after the friction measurement, native plates can absorb kinetic energy from the AFM tip without suffering any damage. These results suggest that plates are formed by a flexible and mechanically resistant two-dimensional network which allows the safe storage of DNA during mitosis.

Local geometry and elasticity in compact chromatin structure

The hierarchical packaging of DNA into chromatin within a eukaryotic nucleus plays a pivotal role in both the accessibility of genomic information and the dynamics of replication. Our work addresses the role of nanoscale physical and geometric properties in determining the structure of chromatin at the mesoscale level. We study the packaging of DNA in chromatin fibers by optimization of regular helical morphologies, considering the elasticity of the linker DNA as well as steric packing of the nucleosomes and linkers. Our model predicts a broad range of preferred helix structures for a fixed linker length of DNA; changing the linker length alters the predicted ensemble. Specifically, we find that the twist registry of the nucleosomes, as set by the internucleosome repeat length, determines the preferred angle between the nucleosomes and the fiber axis. For moderate to long linker lengths, we find a number of energetically comparable configurations with different nucleosome-nucleosome interaction patterns, indicating a potential role for kinetic trapping in chromatin fiber formation. Our results highlight the key role played by DNA elasticity and local geometry in regulating the hierarchical packaging of the genome.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.