Force spectroscopy of chromatin fibers: Extracting energetics and structural information from Monte Carlo simulations

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

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.

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.

Chromatin fiber breaks into clutches under tension and crowding

The arrangement of nucleosomes inside chromatin is of extensive interest. While in vitro experiments have revealed the formation of 30 nm fibers, most in vivo studies have failed to confirm their presence in cell nuclei. To reconcile the diverging experimental findings, we characterized chromatin organization using a residue-level coarse-grained model. The computed force–extension curve matches well with measurements from single-molecule experiments. Notably, we found that a dodeca-nucleosome in the two-helix zigzag conformation breaks into structures with nucleosome clutches and a mix of trimers and tetramers under tension. Such unfolded configurations can also be stabilized through trans interactions with other chromatin chains. Our study suggests that unfolding from chromatin fibers could contribute to the irregularity of in vivo chromatin configurations. We further revealed that chromatin segments with fibril or clutch structures engaged in distinct binding modes and discussed the implications of these inter-chain interactions for a potential sol–gel phase transition.

Histone Modifications, Internucleosome Dynamics, and DNA Stresses: How They Cooperate to “Functionalize” Nucleosomes

Tight packaging of DNA in chromatin severely constrains DNA accessibility and dynamics. In contrast, nucleosomes in active chromatin state are highly flexible, can exchange their histones, and are virtually “transparent” to RNA polymerases, which transcribe through gene bodies at rates comparable to that of naked DNA. Defining mechanisms that revert nucleosome repression, in addition to their value for basic science, is of key importance for the diagnosis and treatment of genetic diseases. Chromatin activity is largely regulated by histone posttranslational modifications, ranging from small chemical groups up to the yet understudied “bulky” ubiquitylation and sumoylation. However, it is to be revealed how histone marks are “translated” to permissive or repressive changes in nucleosomes: it is a general opinion that histone modifications act primarily as “signals” for recruiting the regulatory proteins or as a “neutralizer” of electrostatic shielding of histone tails. Here, we would like to discuss recent evidence suggesting that histone ubiquitylation, in a DNA stress–dependent manner, can directly regulate the dynamics of the nucleosome and their primary structure and can promote nucleosome decomposition to hexasome particles or additionally stabilize nucleosomes against unwrapping. In addition, nucleosome repression/ derepression studies are usually performed with single mononucleosomes as a model. We would like to review and discuss recent findings showing that internucleosomal interactions could strongly modulate the dynamics and rearrangements of nucleosomes. Our hypothesis is that bulky histone modifications, nucleosome inherent dynamics, internucleosome interactions, and DNA torsions could act in cooperation to orchestrate the formation of different dynamic states of arrayed nucleosomes and thus promote chromatin functionality and diversify epigenetic programming methods.

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.

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.

Rigid Basepair Monte Carlo Simulations of One-Start and Two-Start Chromatin Fiber Unfolding by Force

The organization of chromatin in 30 nm fibers remains a topic of debate. Here, we quantify the mechanical properties of the linker DNA and evaluate the impact of these properties on chromatin fiber folding. We extended a rigid basepair DNA model to include (un)wrapping of nucleosomal DNA and (un)stacking of nucleosomes in one-start and two-start chromatin fibers. Monte Carlo simulations that mimic single-molecule force spectroscopy experiments of folded nucleosomal arrays reveal different stages of unfolding as a function of force and are largely consistent with a two-start folding for 167 and one-start folding for 197 nucleosome repeat length fibers. The major insight is that nucleosome unstacking and subsequent unwrapping is not necessary to obtain quantitative agreement with experimental force extension curves up to the overstretching plateau of folded chromatin fibers at 3-5 pN. Nucleosome stacking appears better accommodated in one-start than in two-start conformations, and we suggest that this difference can compensate the increased energy for bending the linker DNA. Overall, these simulations capture the dynamic structure of chromatin fibers while maintaining realistic physical properties of the linker DNA.

Dynamics of Chromatin Fibers: Comparison of Monte Carlo Simulations with Force Spectroscopy

To elucidate conformational dynamics of chromatin fibers, we compared available force-spectroscopy measurements with extensive Monte Carlo simulations of nucleosome arrays under external force. Our coarse-grained model of chromatin includes phenomenological energy terms for the DNA-histone adhesion and the internucleosome stacking interactions. We found that the Monte Carlo fiber ensembles simulated with increasing degrees of DNA unwrapping and the stacking energy 8 kT can account for the intricate force-extension response observed experimentally. Our analysis shows that at low external forces (F < 3.0 picoNewtons), the DNA ends in nucleosomes breathe by ∼10 bp. Importantly, under these conditions, the fiber is highly dynamic, exhibiting continuous unstacking-restacking transitions, allowing accessibility of transcription factors to DNA, while maintaining a relatively compact conformation. Of note, changing the stacking interaction by a few kT, an in silico way to mimic histone modifications, is sufficient to transform an open chromatin state into a compact fiber. The fibers are mostly two-start zigzag folds with rare occurrences of three- to five-start morphologies. The internucleosome stacking is lost during the linear response regime. At the higher forces exceeding 4 picoNewtons, the nucleosome unwrapping becomes stochastic and asymmetric, with one DNA arm opened by ∼55 bp and the other arm only by ∼10 bp. Importantly, this asymmetric unwrapping occurs for any kind of sequence, including the symmetric ones. Our analysis brings new, to our knowledge, insights in dynamics of chromatin modulated by histone epigenetic modifications and molecular motors such as RNA polymerase.

Transfer-matrix calculations of the effects of tension and torque constraints on DNA-protein interactions

Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such proteins is frequently subject to force and torque constraints applied to the DNA. Although the existing experimental techniques allow to exert these type of mechanical constraints on individual DNA biopolymers, their exact effects in regulation of DNA-protein interactions are still not completely understood due to the lack of systematic theoretical methods able to efficiently interpret complex experimental observations. To fill this gap, we have developed a general theoretical framework based on the transfer-matrix calculations that can be used to accurately describe behaviour of DNA-protein interactions under force and torque constraints. Potential applications of the constructed theoretical approach are demonstrated by predicting how these constraints affect the DNA-binding properties of different types of architectural proteins. Obtained results provide important insights into potential physiological functions of mechanical forces in the chromosomal DNA organization by architectural proteins as well as into single-DNA manipulation studies of DNA-protein interactions.

H4 Tails Potentially Produce the Diversity in the Orientation of Two Nucleosomes

Histone tails play an important role in internucleosomal interaction and chromatin compaction. To understand how the H4 tails are involved in the internucleosomal interaction, an adaptively biased molecular dynamics simulation of 63 models of two stacked nucleosomes, each with the H4 tails in different locations, was carried out. This simulation generated a variety of orientations of the separated nucleosomes depending on the formation of the H4 tail bridge between the H4 tails and the DNA of the neighboring nucleosomes. For the models that showed distinctive orientations of the two nucleosomes, the free energies of the separation of the nucleosomes were further investigated using umbrella sampling simulations. The attractive force between the nucleosomes was estimated from the free energies; the force when two H4 tail bridges formed varied from 36 to 63 pN, depending on the formation of the H4 tail-bridge and the interfacial interaction, whereas the force reduced to 15-18 pN after either one of the H4 tail bridges had broken, regardless of the conformation of the H4 tail. Additional simulations of the nucleosomes show that when the H4 tail was truncated, the force between the nucleosomes became repulsive (from-3 to -7 pN). We concluded that the H4 tails potentially produce the diversity in the orientation of the two nucleosomes, which would contribute to the polymorphism of the chromatin structure.

Linking Chromatin Fibers to Gene Folding by Hierarchical Looping

While much is known about DNA structure on the basepair level, this scale represents only a fraction of the structural levels involved in folding the genomic material. With recent advances in experimental and theoretical techniques, a variety of structures have been observed on the fiber, gene, and chromosome levels of genome organization. Here we view chromatin architecture from nucleosomes and fibers to genes and chromosomes, highlighting the rich structural diversity and fiber fluidity emerging from both experimental and theoretical techniques. In this context, we discuss our recently proposed folding mechanism, which we call "hierarchical looping", similar to rope flaking used in mountain climbing, where 10-nm zigzag chromatin fibers are compacted laterally into self-associating loops which then stack and fold in space. We propose that hierarchical looping may act as a bridge between fibers and genes as well as provide a mechanism to relate key features of interphase and metaphase chromosome architecture to genome structural changes. This motif emerged by analysis of ultrastructural internucleosome contact data by electron microscopy-assisted nucleosome interaction capture cross-linking experiments, in combination with mesoscale modeling. We suggest that while the local folding of chromatin can be regulated at the fiber level by adjustment of internal factors such as linker-histone binding affinities, linker DNA lengths, and divalent ion levels, hierarchical looping on the gene level can additionally be controlled by posttranslational modifications and external factors such as polycomb group proteins. From a combination of 3C data and mesoscale modeling, we suggest that hierarchical looping could also play a role in epigenetic gene silencing, as stacked loops may occlude access to transcription start sites. With advances in crystallography, single-molecule in vitro biochemistry, in vivo imaging techniques, and genome-wide contact data experiments, various modeling approaches are allowing for previously unavailable structural interpretation of these data at multiple spatial and temporal scales. An unprecedented level of productivity and opportunity is on the horizon for the chromatin structure field.

On the role of inter-nucleosomal interactions and intrinsic nucleosome dynamics in chromatin function

Evidence is emerging that many diseases result from defects in gene functions, which, in turn, depend on the local chromatin environment of a gene. However, it still remains not fully clear how chromatin activity code is 'translated' to the particular 'activating' or 'repressing' chromatin structural transition. Commonly, chromatin remodeling in vitro was studied using mononucleosomes as a model. However, recent data suggest that structural reorganization of a single mononucleosome is not equal to remodeling of a nucleosome particle under multinucleosomal content - such as, interaction of nucleosomes via flexible histone termini could significantly alter the mode (and the resulting products) of nucleosome structural transitions. It is becoming evident that a nucleosome array does not constitute just a 'polymer' of individual 'canonical' nucleosomes due to multiple inter-nucleosomal interactions which affect nucleosome dynamics and structure. It could be hypothesized, that inter-nucleosomal interactions could act in cooperation with nucleosome inherent dynamics to orchestrate DNA-based processes and promote formation and stabilization of highly-dynamic, accessible structure of a nucleosome array. In the proposed paper we would like to discuss the nucleosome dynamics within the chromatin fiber mainly as it pertains to the roles of the structural changes mediated by inter-nucleosomal interactions.

Stacked thin layers of metaphase chromatin explain the geometry of chromosome rearrangements and banding

The three-dimensional organization of tightly condensed chromatin within metaphase chromosomes has been one of the most challenging problems in structural biology since the discovery of the nucleosome. This study shows that chromosome images obtained from typical banded karyotypes and from different multicolour cytogenetic analyses can be used to gain information about the internal structure of chromosomes. Chromatin bands and the connection surfaces in sister chromatid exchanges and in cancer translocations are planar and orthogonal to the chromosome axis. Chromosome stretching produces band splitting and even the thinnest bands are orthogonal and well defined, indicating that short stretches of DNA can occupy completely the chromosome cross-section. These observations impose strong physical constraints on models that attempt to explain chromatin folding in chromosomes. The thin-plate model, which consists of many stacked layers of planar chromatin perpendicular to the chromosome axis, is compatible with the observed orientation of bands, with the existence of thin bands, and with band splitting; it is also compatible with the orthogonal orientation and planar geometry of the connection surfaces in chromosome rearrangements. The results obtained provide a consistent interpretation of the chromosome structural properties that are used in clinical cytogenetics for the diagnosis of hereditary diseases and cancers.

Partial Unwrapping and Histone Tail Dynamics in Nucleosome Revealed by Coarse-Grained Molecular Simulations

Nucleosomes, basic units of chromatin, are known to show spontaneous DNA unwrapping dynamics that are crucial for transcriptional activation, but its structural details are yet to be elucidated. Here, employing a coarse-grained molecular model that captures residue-level structural details up to histone tails, we simulated equilibrium fluctuations and forced unwrapping of single nucleosomes at various conditions. The equilibrium simulations showed spontaneous unwrapping from outer DNA and subsequent rewrapping dynamics, which are in good agreement with experiments. We found several distinct partially unwrapped states of nucleosomes, as well as reversible transitions among these states. At a low salt concentration, histone tails tend to sit in the concave cleft between the histone octamer and DNA, tightening the nucleosome. At a higher salt concentration, the tails tend to bound to the outer side of DNA or be expanded outwards, which led to higher degree of unwrapping. Of the four types of histone tails, H3 and H2B tail dynamics are markedly correlated with partial unwrapping of DNA, and, moreover, their contributions were distinct. Acetylation in histone tails was simply mimicked by changing their charges, which enhanced the unwrapping, especially markedly for H3 and H2B tails.

Nucleosomes, folding units of chromatin, wrap DNA about 1.75 turns and provide bottlenecks for transcription. Recent experiments showed that nucleosomes are not rigid but dynamic, showing spontaneous and partial unwrapping which is thus important for transcriptional activation. Experimentally, however, one cannot directly watch DNA unwrapping at high resolution. On the other hand, molecular dynamics simulations have high spatio-temporal resolution and thus can be powerful and complementary to experiments. Here, we put forward coarse-grained modeling of protein-DNA interactions at residue-level resolution, which is rather generic and thus can be applied to any protein-DNA complexes. By this method, we could reveal spontaneous and salt-concentration dependent partial unwrapping of DNA from nucleosomes. In addition to consistency with single molecule experiments, the simulation showed multiple and distinct intermediate states of unwrapping. Interestingly, partial unwrapping of DNA is correlated with certain parts of histone tail dynamics. Deleting positive charges in histone tails that mimics histone acetylation facilitated partial unwrapping, most significantly for H3 and H2B.

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.

Quantitative analysis of single-molecule force spectroscopy on folded chromatin fibers

Single-molecule techniques allow for picoNewton manipulation and nanometer accuracy measurements of single chromatin fibers. However, the complexity of the data, the heterogeneity of the composition of individual fibers and the relatively large fluctuations in extension of the fibers complicate a structural interpretation of such force-extension curves. Here we introduce a statistical mechanics model that quantitatively describes the extension of individual fibers in response to force on a per nucleosome basis. Four nucleosome conformations can be distinguished when pulling a chromatin fiber apart. A novel, transient conformation is introduced that coexists with single wrapped nucleosomes between 3 and 7 pN. Comparison of force-extension curves between single nucleosomes and chromatin fibers shows that embedding nucleosomes in a fiber stabilizes the nucleosome by 10 kBT. Chromatin fibers with 20- and 50-bp linker DNA follow a different unfolding pathway. These results have implications for accessibility of DNA in fully folded and partially unwrapped chromatin fibers and are vital for understanding force unfolding experiments on nucleosome arrays.

Forced unraveling of chromatin fibers with nonuniform linker DNA lengths

The chromatin fiber undergoes significant structural changes during the cell's life cycle to modulate DNA accessibility. Detailed mechanisms of such structural transformations of chromatin fibers as affected by various internal and external conditions such as the ionic conditions of the medium, the linker DNA length, and the presence of linker histones, constitute an open challenge. Here we utilize Monte Carlo (MC) simulations of a coarse grained model of chromatin with nonuniform linker DNA lengths as found in vivo to help explain some aspects of this challenge. We investigate the unfolding mechanisms of chromatin fibers with alternating linker lengths of 26-62 bp and 44-79 bp using a series of end-to-end stretching trajectories with and without linker histones and compare results to uniform-linker-length fibers. We find that linker histones increase overall resistance of nonuniform fibers and lead to fiber unfolding with superbeads-on-a-string cluster transitions. Chromatin fibers with nonuniform linker DNA lengths display a more complex, multi-step yet smoother process of unfolding compared to their uniform counterparts, likely due to the existence of a more continuous range of nucleosome-nucleosome interactions. This finding echoes the theme that some heterogeneity in fiber component is biologically advantageous.

Affinity, stoichiometry and cooperativity of heterochromatin protein 1 (HP1) binding to nucleosomal arrays

Heterochromatin protein 1 (HP1) participates in establishing and maintaining heterochromatin via its histone-modification-dependent chromatin interactions. In recent papers HP1 binding to nucleosomal arrays was measured in vitro and interpreted in terms of nearest-neighbour cooperative binding. This mode of chromatin interaction could lead to the spreading of HP1 along the nucleosome chain. Here, we reanalysed previous data by representing the nucleosome chain as a 1D binding lattice and showed how the experimental HP1 binding isotherms can be explained by a simpler model without cooperative interactions between neighboring HP1 dimers. Based on these calculations and spatial models of dinucleosomes and nucleosome chains, we propose that binding stoichiometry depends on the nucleosome repeat length (NRL) rather than protein interactions between HP1 dimers. According to our calculations, more open nucleosome arrays with long DNA linkers are characterized by a larger number of binding sites in comparison to chains with a short NRL. Furthermore, we demonstrate by Monte Carlo simulations that the NRL dependent folding of the nucleosome chain can induce allosteric changes of HP1 binding sites. Thus, HP1 chromatin interactions can be modulated by the change of binding stoichiometry and the type of binding to condensed (methylated) and non-condensed (unmethylated) nucleosome arrays in the absence of direct interactions between HP1 dimers.

The polymorphisms of the chromatin fiber

In eukaryotes, the genome is packed into chromosomes, each consisting of large polymeric fibers made of DNA bound with proteins (mainly histones) and RNA molecules. The nature and precise 3D organization of this fiber has been a matter of intense speculations and debates. In the emerging picture, the local chromatin state plays a critical role in all fundamental DNA transactions, such as transcriptional control, DNA replication or repair. However, the molecular and structural mechanisms involved remain elusive. The purpose of this review is to give an overview of the tremendous efforts that have been made for almost 40 years to build physiologically relevant models of chromatin structure. The motivation behind building such models was to shift our representation and understanding of DNA transactions from a too simplistic 'naked DNA' view to a more realistic 'coated DNA' view, as a step towards a better framework in which to interpret mechanistically the control of genetic expression and other DNA metabolic processes. The field has evolved from a speculative point of view towards in vitro biochemistry and in silico modeling, but is still longing for experimental in vivo validations of the proposed structures or even proof of concept experiments demonstrating a clear role of a given structure in a metabolic transaction. The mere existence of a chromatin fiber as a relevant biological entity in vivo has been put into serious questioning. Current research is suggesting a possible reconciliation between theoretical studies and experiments, pointing towards a view where the polymorphic and dynamic nature of the chromatin fiber is essential to support its function in genome metabolism.

Physicochemical modifications of histones and their impact on epigenomics

The study of histone post-translational modifications (PTMs) has made extraordinary progress over the past few years and many epigenetic modifications have been identified and found to be associated with fundamental biological processes and pathological conditions. Most histone-modifying enzymes produce specific covalent modifications on histone tails that, taken together, elicit complex and concerted processes. An even higher level of complexity is generated by the action of small molecules that are able to modulate pharmacologically epigenetic enzymes and interfere with these biochemical mechanisms. In this article, we provide an overview of histone PTMs by reviewing and discussing them in terms of their physicochemical properties, emphasizing these concepts in view of recent research efforts to elucidate epigenetic mechanisms and devise future epigenetic drugs.

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.

Establishing epigenetic domains via chromatin-bound histone modifiers

The eukaryotic nucleus harbors the DNA genome, which associates with histones and other chromosomal proteins into a complex referred to as chromatin. It provides an additional layer of so-called epigenetic information via histone modifications and DNA methylation on top of the DNA sequence that determines the cell's active gene expression program. The nucleus is devoid of internal organelles separated by membranes. Thus, free diffusive transport of proteins and RNA can occur throughout the space accessible for a given macromolecule. At the same time, chromatin is partitioned into different specialized structures such as nucleoli, chromosome territories, and heterochromatin domains that serve distinct functions. Here, we address the question of how the activity of chromatin-modifying enzymes is confined to chromatin subcompartments. We discuss mechanisms for establishing activity gradients of diffusive chromatin-modifying enzymes that could give rise to distinct chromatin domains within the cell nucleus. Interestingly, such gradients might directly result from immobilization of the enzymes on the flexible chromatin chain. Thus, locus-specific tethering of these enzymes to chromatin could have the potential to establish, maintain, or modulate epigenetic patterns of characteristic domain size.

Insights into chromatin fibre structure by in vitro and in silico single-molecule stretching experiments

The detailed structure and dynamics of the chromatin fibre and their relation to gene regulation represent important open biological questions. Recent advances in single-molecule force spectroscopy experiments have addressed these questions by directly measuring the forces that stabilize and alter the folded states of chromatin, and by investigating the mechanisms of fibre unfolding. We present examples that demonstrate how complementary modelling approaches have helped not only to interpret the experimental findings, but also to advance our knowledge of force-induced events such as unfolding of chromatin with dynamically bound linker histones and 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.

Pulling chromatin apart: Unstacking or Unwrapping?

Background

Understanding the mechanical properties of chromatin is an essential step towards deciphering the physical rules of gene regulation. In the past ten years, many single molecule experiments have been carried out, and high resolution measurements of the chromatin fiber stiffness are now available. Simulations have been used in order to link those measurements with structural cues, but so far no clear agreement among different groups has been reached.

Results

We revisit here some of the most precise experimental results obtained with carefully reconstituted fibers.

Conclusions

We show that the mechanical properties of the chromatin fiber can be quantitatively accounted for by the stiffness of the DNA molecule and the 3D structure of the chromatin fiber.

Distinct contributions of MSL complex subunits to the transcriptional enhancement responsible for dosage compensation in Drosophila

The regulatory mechanism of dosage compensation is the paramount example of epigenetic regulation at the chromosomal level. In Drosophila, this mechanism, designed to compensate for the difference in the dosage of X-linked genes between the sexes, depends on the MSL complex that enhances the transcription of the single dose of these genes in males. We have investigated the function of various subunits of the complex in mediating dosage compensation. Our results confirm that the highly enriched specific acetylation of histone H4 at lysine 16 of compensated genes by the histone acetyl transferase subunit MOF induces a more disorganized state of their chromatin. We have determined that the association of the MSL complex reduces the level of negative supercoiling of the deoxyribonucleic acid of compensated genes, and we have defined the role that the other subunits of the complex play in this topological modification. Lastly, we have analyzed the potential contribution of ISWI-containing remodeling complexes to the architecture of compensated chromatin, and we suggest a role for this remodeling factor in dosage compensation.

Crucial role of dynamic linker histone binding and divalent ions for DNA accessibility and gene regulation revealed by mesoscale modeling of oligonucleosomes

Monte Carlo simulations of a mesoscale model of oligonucleosomes are analyzed to examine the role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to further interpret noted chromatin fiber softening by dynamic LH in monovalent salt conditions. We find that divalent ions produce a fiber stiffening effect that competes with, but does not overshadow, the dramatic softening triggered by dynamic-LH behavior. Indeed, we find that in typical in vivo conditions, dynamic-LH binding/unbinding reduces fiber stiffening dramatically (by a factor of almost 5, as measured by the elasticity modulus) compared with rigidly fixed LH, and also the force needed to initiate chromatin unfolding, making it consistent with those of molecular motors. Our data also show that, during unfolding, divalent ions together with LHs induce linker-DNA bending and DNA–DNA repulsion screening, which guarantee formation of heteromorphic superbeads-on-a-string structures that combine regions of loose and compact fiber independently of the characteristics of the LH–core bond. These structures might be important for gene regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding, either globally or locally, in the presence of divalent ions, might constitute a mechanism for regulation of gene expression.

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.

Dissecting DNA-histone interactions in the nucleosome by molecular dynamics simulations of DNA unwrapping

The nucleosome complex of DNA wrapped around a histone protein octamer organizes the genome of eukaryotes and regulates the access of protein factors to the DNA. We performed molecular dynamics simulations of the nucleosome in explicit water to study the dynamics of its histone-DNA interactions. A high-resolution histone-DNA interaction map was derived that revealed a five-nucleotide periodicity, in which the two DNA strands of the double helix made alternating contacts. On the 100-ns timescale, the histone tails mostly maintained their initial positions relative to the DNA, and the spontaneous unwrapping of DNA was limited to 1-2 basepairs. In steered molecular dynamics simulations, external forces were applied to the linker DNA to investigate the unwrapping pathway of the nucleosomal DNA. In comparison with a nucleosome without the unstructured N-terminal histone tails, the following findings were obtained: 1), Two main barriers during unwrapping were identified at DNA position ±70 and ±45 basepairs relative to the central DNA basepair at the dyad axis. 2), DNA interactions of the histone H3 N-terminus and the histone H2A C-terminus opposed the initiation of unwrapping. 3), The N-terminal tails of H2A, H2B, and H4 counteracted the unwrapping process at later stages and were essential determinants of nucleosome dynamics. Our detailed analysis of DNA-histone interactions revealed molecular mechanisms for modulating access to nucleosomal DNA via conformational rearrangements of its structure.