The effect of internucleosomal interaction on folding of the chromatin fiber

Regulation of chromatin architecture by protein binding: insights from molecular modeling

Histone and non-histone proteins play key roles in the activation and repression of genes. In addition to experimental studies of their regulation of gene expression, molecular modeling at the nucleosome, chromatin, and chromosome levels can contribute insights into the molecular mechanisms involved. In this review, we provide an overview for protein-bound chromatin modeling, and describe how our group has integrated protein binding into genome systems across the scales, from all-atom to coarse-grained models, using explicit to implicit descriptions. We describe the associated applications to protein binding effects and biological mechanisms of genome folding and gene regulation. We end by illustrating the application of machine learning tools like AlphaFold2 to proteins relevant to chromatin systems.

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.

True-to-scale DNA-density maps correlate with major accessibility differences between active and inactive chromatin

Chromatin compaction differences may have a strong impact on accessibility of individual macromolecules and macromolecular assemblies to their DNA target sites. Estimates based on fluorescence microscopy with conventional resolution, however, suggest only modest compaction differences (∼2-10×) between the active nuclear compartment (ANC) and inactive nuclear compartment (INC). Here, we present maps of nuclear landscapes with true-to-scale DNA densities, ranging from <5 to >300 Mbp/μm3. Maps are generated from individual human and mouse cell nuclei with single-molecule localization microscopy at ∼20 nm lateral and ∼100 nm axial optical resolution and are supplemented by electron spectroscopic imaging. Microinjection of fluorescent nanobeads with sizes corresponding to macromolecular assemblies for transcription into nuclei of living cells demonstrates their localization and movements within the ANC and exclusion from the INC.

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.

Beyond Sequence: Internucleosomal Interactions Dominate Array Assembly

The organization of the nucleosome array is a critical component of the chromatin assembly into higher order structure as well as its function. Here, we investigated the contributions of the DNA sequence and internucleosomal interactions on the organization of the nucleosomal arrays in compact structures using atomic force microscopy. We assembled nucleosomes on DNA substrates allowing for the formation of tetranucleosomes. We found that nucleosomes are capable of close positioning with no discernible space between them, even in the case of assembled dinucleosomes. This morphology of the array is in contrast with that observed for arrays assembled with repeats of the nucleosome positioning motifs separated by uniform spacers. Simulated assembly of tetranucleosomes by random placement along the substrates revealed that nucleosome array compaction is promoted by the interaction of the nucleosomes. We developed a theoretical model to account for the role of DNA sequence and internucleosomal interactions in the formation of the nucleosome structures. These findings suggest that, in the chromatin assembly, the affinity of the nucleosomes to the DNA sequence and the strengths of the internucleosomal interactions are the two major factors defining the compactness of the chromatin.

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.

The Effects of Histone H2B Ubiquitylations on the Nucleosome Structure and Internucleosomal Interactions

Eukaryotic gene compaction takes place at multiple levels to package DNA to chromatin and chromosomes. Two of the most fundamental levels of DNA packaging are at the nucleosome and dinucleosome stacks. The nucleosome is the basic gene-packing unit and is composed of DNA wrapped around a histone core. Nucleosomes stack with one another for further compaction of DNA. The first stacking step leads to dinucleosome formation, which is driven by internucleosomal interactions between various parts of two nucleosomes. Histone proteins are rich targets for post-translational modifications, some of which affect the structure of the nucleosome and the interactions between nucleosomes. These effects are often implicated in the regulation of various genomic transactions. In particular, histone H2B ubiquitylation has been associated with facilitated transcription and hexasome formation. Here, we employed semi-synthetically ubiquitylated histone H2B and single-molecule FRET to investigate the effects of H2B ubiquitylations at lysine 34 (H2BK34) and lysine 120 (H2BK120) on the structure of the nucleosome and the interactions between two nucleosomes. Our results suggest that H2BK34 ubiquitylation widens the DNA gyre gap in the nucleosome and stabilizes long- and short-range internucleosomal interactions while H2BK120 ubiquitylation does not affect the nucleosome structure or internucleosomal interactions. These results suggest potential roles for H2B ubiquitylations in facilitated transcription and hexasome formation while maintaining the structural integrity of chromatin.

A Bottom-Up Coarse-Grained Model for Nucleosome-Nucleosome Interactions with Explicit Ions

The nucleosome core particle (NCP) is a large complex of 145-147 base pairs of DNA and eight histone proteins and is the basic building block of chromatin that forms the chromosomes. Here, we develop a coarse-grained (CG) model of the NCP derived through a systematic bottom-up approach based on underlying all-atom MD simulations to compute the necessary CG interactions. The model produces excellent agreement with known structural features of the NCP and gives a realistic description of the nucleosome-nucleosome attraction in the presence of multivalent cations (Mg(H₂O)₆²⁺ or Co(NH₃)₆³⁺) for systems comprising 20 NCPs. The results of the simulations reveal structural details of the NCP-NCP interactions unavailable from experimental approaches, and this model opens the prospect for the rigorous modeling of chromatin fibers.

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.

Biophysics is reshaping our perception of the epigenome: from DNA-level to high-throughput studies

Epigenetic research holds great promise to advance our understanding of biomarkers and regulatory processes in health and disease. An increasing number of new approaches, ranging from molecular to biophysical analyses, enable identifying epigenetic changes on the level of a single gene or the whole epigenome. The aim of this review is to highlight how the field is shifting from completely molecular-biology-driven solutions to multidisciplinary strategies including more reliance on biophysical analysis tools. Biophysics not only offers technical advancements in imaging or structure analysis but also helps to explore regulatory interactions. New computational methods are also being developed to meet the demand of growing data volumes and their processing. Therefore, it is important to capture these new directions in epigenetics from a biophysical perspective and discuss current challenges as well as multiple applications of biophysical methods and tools. Specifically, we gradually introduce different biophysical research methods by first considering the DNA-level information and eventually higher-order chromatin structures. Moreover, we aim to highlight that the incorporation of bioinformatics, machine learning, and artificial intelligence into biophysical analysis allows gaining new insights into complex epigenetic processes. The gained understanding has already proven useful in translational and clinical research providing better patient stratification options or new therapeutic insights. Together, this offers a better readiness to transform bench-top experiments into industrial high-throughput applications with a possibility to employ developed methods in clinical practice and diagnostics.

A glitch in the snitch: the role of linker histone H1 in shaping the epigenome in normal and diseased cells

Histone H1s or the linker histones are a family of dynamic chromatin compacting proteins that are essential for higher-order chromatin organization. These highly positively charged proteins were previously thought to function solely as repressors of transcription. However, over the last decade, there is a growing interest in understanding this multi-protein family, finding that not all variants act as repressors. Indeed, the H1 family members appear to have distinct affinities for chromatin and may potentially affect distinct functions. This would suggest a more nuanced contribution of H1 to chromatin organization. The advent of new technologies to probe H1 dynamics in vivo, combined with powerful computational biology, and in vitro imaging tools have greatly enhanced our knowledge of the mechanisms by which H1 interacts with chromatin. This family of proteins can be metaphorically compared to the Golden Snitch from the Harry Potter series, buzzing on and off several regions of the chromatin, in combat with competing transcription factors and chromatin remodellers, thereby critical to the epigenetic endgame on short and long temporal scales in the life of the nucleus. Here, we summarize recent efforts spanning structural, computational, genomic and genetic experiments which examine the linker histone as an unseen architect of chromatin fibre in normal and diseased cells and explore unanswered fundamental questions in the field.

Protein intrinsic disorder on a dynamic nucleosomal landscape

The complex nucleoprotein landscape of the eukaryotic cell nucleus is rich in dynamic proteins that lack a stable three-dimensional structure. Many of these intrinsically disordered proteins operate directly on the first fundamental level of genome compaction: the nucleosome. Here we give an overview of how disordered interactions with and within nucleosomes shape the dynamics, architecture, and epigenetic regulation of the genetic material, controlling cellular transcription patterns. We highlight experimental and computational challenges in the study of protein disorder and illustrate how integrative approaches are increasingly unveiling the fine details of nuclear interaction networks. We finally dissect sequence properties encoded in disordered regions and assess common features of disordered nucleosome-binding proteins. As drivers of many critical biological processes, disordered proteins are integral to a comprehensive molecular view of the dynamic nuclear milieu.

Tetranucleosome Interactions Drive Chromatin Folding

The multiscale organizational structure of chromatin in eukaryotic cells is instrumental to DNA transcription, replication, and repair. At mesoscopic length scales, nucleosomes pack in a manner that serves to regulate gene expression through condensation and expansion of the genome. The particular structures that arise and their respective thermodynamic stabilities, however, have yet to be fully resolved. In this study, we combine molecular modeling using the 1CPN mesoscale model of chromatin with nonlinear manifold learning to identify and characterize the structure and free energy of metastable states of short chromatin segments comprising between 4- and 16-nucleosomes. Our results reveal the formation of two previously characterized tetranucleosomal conformations, the "α-tetrahedron" and the "β-rhombus", which have been suggested to play an important role in the accessibility of DNA and, respectively, induce local chromatin compaction or elongation. The spontaneous formation of these motifs is potentially responsible for the slow nucleosome dynamics observed in experimental studies. Increases of the nucleosome repeat length are accompanied by more pronounced structural irregularity and flexibility and, ultimately, a dynamic liquid-like behavior that allows for frequent structural reorganization. Our findings indicate that tetranucleosome motifs are intrinsically stable structural states, driven by local internucleosomal interactions, and support a mechanistic picture of chromatin packing, dynamics, and accessibility that is strongly influenced by emergent local mesoscale structure.

Elucidating the influence of linker histone variants on chromatosome dynamics and energetics

Linker histones are epigenetic regulators that bind to nucleosomes and alter chromatin structures and dynamics. Biophysical studies have revealed two binding modes in the linker histone/nucleosome complex, the chromatosome, where the linker histone is either centered on or askew from the dyad axis. Each has been posited to have distinct effects on chromatin, however the molecular and thermodynamic mechanisms that drive them and their dependence on linker histone compositions remain poorly understood. We present molecular dynamics simulations of chromatosomes with the globular domain of two linker histone variants, generic H1 (genGH1) and H1.0 (GH1.0), to determine how their differences influence chromatosome structures, energetics and dynamics. Results show that both unbound linker histones adopt a single compact conformation. Upon binding, DNA flexibility is reduced, resulting in increased chromatosome compaction. While both variants enthalpically favor on-dyad binding, energetic benefits are significantly higher for GH1.0, suggesting that GH1.0 is more capable than genGH1 of overcoming the large entropic reduction required for on-dyad binding which helps rationalize experiments that have consistently demonstrated GH1.0 in on-dyad states but that show genGH1 in both locations. These simulations highlight the thermodynamic basis for different linker histone binding motifs, and details their physical and chemical effects on chromatosomes.

Chromatin Compaction Multiscale Modeling: A Complex Synergy Between Theory, Simulation, and Experiment

Understanding the mechanisms that trigger chromatin compaction, its patterns, and the factors they depend on, is a fundamental and still open question in Biology. Chromatin compacts and reinforces DNA and is a stable but dynamic structure, to make DNA accessible to proteins. In recent years, computational advances have provided larger amounts of data and have made large-scale simulations more viable. Experimental techniques for the extraction and reconstitution of chromatin fibers have improved, reinvigorating theoretical and experimental interest in the topic and stimulating debate on points previously considered as certainties regarding chromatin. A great assortment of approaches has emerged, from all-atom single-nucleosome or oligonucleosome simulations to various degrees of coarse graining, to polymer models, to fractal-like structures and purely topological models. Different fiber-start patterns have been studied in theory and experiment, as well as different linker DNA lengths. DNA is a highly charged macromolecule, making ionic and electrostatic interactions extremely important for chromatin topology and dynamics. Indeed, the repercussions of varying ionic concentration have been extensively examined at the computational level, using all-atom, coarse-grained, and continuum techniques. The presence of high-curvature AT-rich segments in DNA can cause conformational variations, attesting to the fact that the role of DNA is both structural and electrostatic. There have been some tentative attempts to describe the force fields governing chromatin conformational changes and the energy landscapes of these transitions, but the intricacy of the system has hampered reaching a consensus. The study of chromatin conformations is an intrinsically multiscale topic, influenced by a wide range of biological and physical interactions, spanning from the atomic to the chromosome level. Therefore, powerful modeling techniques and carefully planned experiments are required for an overview of the most relevant phenomena and interactions. The topic provides fertile ground for interdisciplinary studies featuring a synergy between theoretical and experimental scientists from different fields and the cross-validation of respective results, with a multi-scale perspective. Here, we summarize some of the most representative approaches, and focus on the importance of electrostatics and solvation, often overlooked aspects of chromatin modeling.

Chromatosome Structure and Dynamics from Molecular Simulations

Chromatosomes are fundamental units of chromatin structure that are formed when a linker histone protein binds to a nucleosome. The positioning of the linker histone on the nucleosome influences the packing of chromatin. Recent simulations and experiments have shown that chromatosomes adopt an ensemble of structures that differ in the geometry of the linker histone-nucleosome interaction. In this article we review the application of Brownian, Monte Carlo, and molecular dynamics simulations to predict the structure of linker histone-nucleosome complexes, to study the binding mechanisms involved, and to predict how this binding affects chromatin fiber structure. These simulations have revealed the sensitivityof the chromatosome structure to variations in DNA and linker histone sequence, as well as to posttranslational modifications, thereby explaining the structural variability observed in experiments. We propose that a concerted application of experimental and computational approaches will reveal the determinants of chromatosome structural variability and how it impacts chromatin packing.

Sensitive effect of linker histone binding mode and subtype on chromatin condensation

The complex role of linker histone (LH) on chromatin compaction regulation has been highlighted by recent discoveries of the effect of LH binding variability and isoforms on genome structure and function. Here we examine the effect of two LH variants and variable binding modes on the structure of chromatin fibers. Our mesoscale modeling considers oligonucleosomes with H1C and H1E, bound in three different on and off-dyad modes, and spanning different LH densities (0.5–1.6 per nucleosome), over a wide range of physiologically relevant nucleosome repeat lengths (NRLs). Our studies reveal an LH-variant and binding-mode dependent heterogeneous ensemble of fiber structures with variable packing ratios, sedimentation coefficients, and persistence lengths. For maximal compaction, besides dominantly interacting with parental DNA, LHs must have strong interactions with nonparental DNA and promote tail/nonparental core interactions. An off-dyad binding of H1E enables both; others compromise compaction for bendability. We also find that an increase of LH density beyond 1 is best accommodated in chromatosomes with one on-dyad and one off-dyad LH. We suggest that variable LH binding modes and concentrations are advantageous, allowing tunable levels of chromatin condensation and DNA accessibility/interactions. Thus, LHs add another level of epigenetic regulation of chromatin.

Irregular Chromatin: Packing Density, Fiber Width, and Occurrence of Heterogeneous Clusters

How chromatin is folded on the length scale of a gene is an open question. Recent experiments have suggested that, in vivo, chromatin is folded in an irregular manner and not as an ordered fiber with a width of 30 nm that is expected from theories of higher order packaging. Using computational methods, we examine how the interplay between DNA-bending nonhistone proteins, histone tails, intrachromatin electrostatic, and other interactions decide the nature of the packaging of chromatin. We show that although the DNA-bending nonhistone proteins make the chromatin irregular, they may not alter the packing density and size of the fiber. We find that the length of the interacting region and intrachromatin electrostatic interactions influence the packing density, clustering of nucleosomes, and the width of the chromatin fiber. Our results suggest that the heterogeneity in the interaction pattern will play an important role in deciding the nature of the packaging of chromatin.

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.

Chromatin Higher-Order Folding: A Perspective with Linker DNA Angles

The mechanism by which the "beads-on-a-string" nucleosome chain folds into various higher-order chromatin structures in eukaryotic cell nuclei is still poorly understood. The various models depicting higher-order chromatin as regular helical fibers and the very opposite "polymer melt" theory imply that interactions between nucleosome "beads" make the main contribution to the chromatin compaction. Other models in which the geometry of linker DNA "strings" entering and exiting the nucleosome define the three-dimensional structure predict that small changes in the linker DNA configuration may strongly affect nucleosome chain folding and chromatin higher-order structure. Among those studies, the cross-disciplinary approach pioneered by Jörg Langowski that combines computational modeling with biophysical and biochemical experiments was most instrumental for understanding chromatin higher-order structure in vitro. Strikingly, many recent studies, including genome-wide nucleosome interaction mapping and chromatin imaging, show an excellent agreement with the results of three-dimensional computational modeling based on the primary role of linker DNA geometry in chromatin compaction. This perspective relates nucleosome array models with experimental studies of nucleosome array folding in vitro and in situ. I argue that linker DNA configuration plays a key role in determining nucleosome chain flexibility, topology, and propensity for self-association, thus providing new implications for regulation of chromatin accessibility to DNA binding factors and RNA transcription machinery as well as long-range communications between distant genomic sites.

Uncovering the forces between nucleosomes using DNA origami

Revealing the energy landscape for nucleosome association may contribute to the understanding of higher-order chromatin structures and their impact on genome regulation. We accomplish this in a direct measurement by integrating two nucleosomes into a DNA origami-based force spectrometer, which enabled subnanometer-resolution measurements of nucleosome-nucleosome distance frequencies via single-particle electron microscopy imaging. From the data, we derived the Boltzmann-weighted distance-dependent energy landscape for nucleosome pair interactions. We find a shallow but long-range (~6 nm) attractive nucleosome pair potential with a minimum of -1.6 kcal/mol close to direct contact distances. The relative nucleosome orientation had little influence, but histone H4 acetylation or removal of histone tails drastically decreased the interaction strength. Because of the weak and shallow pair potential, higher-order nucleosome assemblies will be compliant and experience dynamic shape fluctuations in the absence of additional cofactors. Our results contribute to a more accurate description of chromatin and our force spectrometer provides a powerful tool for the direct and high-resolution study of molecular interactions using imaging techniques.

Conditions for positioning of nucleosomes on DNA

Positioning of nucleosomes along a eukaryotic genome plays an important role in its organization and regulation. There are many different factors affecting the location of nucleosomes. Some can be viewed as preferential binding of a single nucleosome to different locations along the DNA and some as interactions between neighboring nucleosomes. In this study, we analyze positioning of nucleosomes and derive conditions for their good positioning. Using analytic and numerical approaches we find that, if the binding preferences are very weak, an interplay between the interactions and the binding preferences is essential for a good positioning of nucleosomes, especially on correlated energy landscapes. Analyzing the empirical energy landscape, we conclude that good positioning of nucleosomes in vivo is possible only if they strongly interact. In this case, our model, predicting long-length-scale fluctuations of nucleosomes' occupancy along the DNA, accounts well for the empirical observations.

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 Proportion of Chromatin Graded between Closed and Open States Determines the Level of Transcripts Derived from Distinct Promoters in the CYP19 Gene

The human CYP19 gene encodes aromatase, which converts androgens to estrogens. CYP19 mRNA variants are transcribed mainly from three promoters. Quantitative RT-PCR was used to measure the relative amounts of each of the three transcripts and determine the on/off state of the promoters. While some of the promoters were silent, CYP19 mRNA production differed among the other promoters, whose estimated transcription levels were 0.001% to 0.1% of that of the TUBB control gene. To investigate the structural aspects of chromatin that were responsible for this wide range of activity of the CYP19 promoters, we used a fractionation protocol, designated SEVENS, which sequentially separates densely packed nucleosomes from dispersed nucleosomes. The fractional distribution of each inactive promoter showed a similar pattern to that of the repressed reference loci; the inactive regions were distributed toward lower fractions, in which closed chromatin comprising packed nucleosomes was enriched. In contrast, active CYP19 promoters were raised toward upper fractions, including dispersed nucleosomes in open chromatin. Importantly, these active promoters were moderately enriched in the upper fractions as compared to active reference loci, such as the TUBB promoter; the proportion of open chromatin appeared to be positively correlated to the promoter strength. These results, together with ectopic transcription accompanied by an increase in the proportion of open chromatin in cells treated with an H3K27me inhibitor, indicate that CYP19 mRNA could be transcribed from a promoter in which chromatin is shifted toward an open state in the equilibrium between closed and open chromatin.

Ubiquitous human 'master' origins of replication are encoded in the DNA sequence via a local enrichment in nucleosome excluding energy barriers

As the elementary building block of eukaryotic chromatin, the nucleosome is at the heart of the compromise between the necessity of compacting DNA in the cell nucleus and the required accessibility to regulatory proteins. The recent availability of genome-wide experimental maps of nucleosome positions for many different organisms and cell types has provided an unprecedented opportunity to elucidate to what extent the DNA sequence conditions the primary structure of chromatin and in turn participates in the chromatin-mediated regulation of nuclear functions, such as gene expression and DNA replication. In this study, we use in vivo and in vitro genome-wide nucleosome occupancy data together with the set of nucleosome-free regions (NFRs) predicted by a physical model of nucleosome formation based on sequence-dependent bending properties of the DNA double-helix, to investigate the role of intrinsic nucleosome occupancy in the regulation of the replication spatio-temporal programme in human. We focus our analysis on the so-called replication U/N-domains that were shown to cover about half of the human genome in the germline (skew-N domains) as well as in embryonic stem cells, somatic and HeLa cells (mean replication timing U-domains). The 'master' origins of replication (MaOris) that border these megabase-sized U/N-domains were found to be specified by a few hundred kb wide regions that are hyper-sensitive to DNase I cleavage, hypomethylated, and enriched in epigenetic marks involved in transcription regulation, the hallmarks of localized open chromatin structures. Here we show that replication U/N-domain borders that are conserved in all considered cell lines have an environment highly enriched in nucleosome-excluding-energy barriers, suggesting that these ubiquitous MaOris have been selected during evolution. In contrast, MaOris that are cell-type-specific are mainly regulated epigenetically and are no longer favoured by a local abundance of intrinsic NFRs encoded in the DNA sequence. At the smaller few hundred bp scale of gene promoters, CpG-rich promoters of housekeeping genes found nearby ubiquitous MaOris as well as CpG-poor promoters of tissue-specific genes found nearby cell-type-specific MaOris, both correspond to in vivo NFRs that are not coded as nucleosome-excluding-energy barriers. Whereas the former promoters are likely to correspond to high occupancy transcription factor binding regions, the latter are an illustration that gene regulation in human is typically cell-type-specific.

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.

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.

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.

DNA of a circular minichromosome linearized by restriction enzymes or other reagents is resistant to further cleavage: an influence of chromatin topology on the accessibility of DNA

The accessibility of DNA in chromatin is an essential factor in regulating its activities. We studied the accessibility of the DNA in a ∼170 kb circular minichromosome to DNA-cleaving reagents using pulsed-field gel electrophoresis and fibre-fluorescence in situ hybridization on combed DNA molecules. Only one of several potential sites in the minichromosome DNA was accessible to restriction enzymes in permeabilized cells, and in growing cells only a single site at an essentially random position was cut by poisoned topoisomerase II, neocarzinostatin and γ-radiation, which have multiple potential cleavage sites; further sites were then inaccessible in the linearized minichromosomes. Sequential exposure to combinations of these reagents also resulted in cleavage at only a single site. Minichromosome DNA containing single-strand breaks created by a nicking endonuclease to relax any unconstrained superhelicity was also cut at only a single position by a restriction enzyme. Further sites became accessible after ≥95% of histones H2A, H2B and H1, and most non-histone proteins were extracted. These observations suggest that a global rearrangement of the three-dimensional packing and interactions of nucleosomes occurs when a circular minichromosome is linearized and results in its DNA becoming inaccessible to probes.

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.

New insights into nucleosome and chromatin structure: an ordered state or a disordered affair?

The compaction of genomic DNA into chromatin has profound implications for the regulation of key processes such as transcription, replication and DNA repair. Nucleosomes, the repeating building blocks of chromatin, vary in the composition of their histone protein components. This is the result of the incorporation of variant histones and post-translational modifications of histone amino acid side chains. The resulting changes in nucleosome structure, stability and dynamics affect the compaction of nucleosomal arrays into higher-order structures. It is becoming clear that chromatin structures are not nearly as uniform and regular as previously assumed. This implies that chromatin structure must also be viewed in the context of specific biological functions.

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.

The effect of linker histone's nucleosome binding affinity on chromatin unfolding mechanisms

Eukaryotic gene activation requires selective unfolding of the chromatin fiber to access the DNA for processes such as DNA transcription, replication, and repair. Mutation/modification experiments of linker histone (LH) H1 suggest the importance of dynamic mechanisms for LH binding/dissociation, but the effects on chromatin's unfolding pathway remain unclear. Here we investigate the stretching response of chromatin fibers by mesoscale modeling to complement single-molecule experiments, and present various unfolding mechanisms for fibers with different nucleosome repeat lengths (NRLs) with/without LH that are fixed to their cores or bind/unbind dynamically with different affinities. Fiber softening occurs for long compared to short NRL (due to facile stacking rearrangements), dynamic compared to static LH/core binding as well as slow rather than fast dynamic LH rebinding (due to DNA stem destabilization), and low compared to high LH concentration (due to DNA stem inhibition). Heterogeneous superbead constructs--nucleosome clusters interspersed with extended fiber regions--emerge during unfolding of medium-NRL fibers and may be related to those observed experimentally. Our work suggests that fast and slow LH binding pools, present simultaneously in vivo, might act cooperatively to yield controlled fiber unfolding at low forces. Medium-NRL fibers with multiple dynamic LH pools offer both flexibility and selective DNA exposure, and may be evolutionarily suitable to regulate chromatin architecture and gene expression.

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.

From crystal and NMR structures, footprints and cryo-electron-micrographs to large and soft structures: nanoscale modeling of the nucleosomal stem

The interaction of histone H1 with linker DNA results in the formation of the nucleosomal stem structure, with considerable influence on chromatin organization. In a recent paper [Syed,S.H., Goutte-Gattat,D., Becker,N., Meyer,S., Shukla,M.S., Hayes,J.J., Everaers,R., Angelov,D., Bednar,J. and Dimitrov,S. (2010) Single-base resolution mapping of H1-nucleosome interactions and 3D organization of the nucleosome. Proc. Natl Acad. Sci. USA, 107, 9620-9625], we published results of biochemical footprinting and cryo-electron-micrographs of reconstituted mono-, di- and tri-nucleosomes, for H1 variants with different lengths of the cationic C-terminus. Here, we present a detailed account of the analysis of the experimental data and we include thermal fluctuations into our nano-scale model of the stem structure. By combining (i) crystal and NMR structures of the nucleosome core particle and H1, (ii) the known nano-scale structure and elasticity of DNA, (iii) footprinting information on the location of protected sites on the DNA backbone and (iv) cryo-electron micrographs of reconstituted tri-nucleosomes, we arrive at a description of a polymorphic, hierarchically organized stem with a typical length of 20 ± 2 base pairs. A comparison to linker conformations inferred for poly-601 fibers with different linker lengths suggests, that intra-stem interactions stabilize and facilitate the formation of dense chromatin fibers.

Biomolecularmodeling and simulation: a field coming of age

We assess the progress in biomolecular modeling and simulation, focusing on structure prediction and dynamics, by presenting the field’s history, metrics for its rise in popularity, early expressed expectations, and current significant applications. The increases in computational power combined with improvements in algorithms and force fields have led to considerable success, especially in protein folding, specificity of ligand/biomolecule interactions, and interpretation of complex experimental phenomena (e.g. NMR relaxation, protein-folding kinetics and multiple conformational states) through the generation of structural hypotheses and pathway mechanisms. Although far from a general automated tool, structure prediction is notable for proteins and RNA that preceded the experiment, especially by knowledge-based approaches. Thus, despite early unrealistic expectations and the realization that computer technology alone will not quickly bridge the gap between experimental and theoretical time frames, ongoing improvements to enhance the accuracy and scope of modeling and simulation are propelling the field onto a productive trajectory to become full partner with experiment and a field on its own right.

Hierarchies in eukaryotic genome organization: Insights from polymer theory and simulations

Eukaryotic genomes possess an elaborate and dynamic higher-order structure within the limiting confines of the cell nucleus. Knowledge of the physical principles and the molecular machinery that govern the 3D organization of this structure and its regulation are key to understanding the relationship between genome structure and function. Elegant microscopy and chromosome conformation capture techniques supported by analysis based on polymer models are important steps in this direction. Here, we review results from these efforts and provide some additional insights that elucidate the relationship between structure and function at different hierarchical levels of genome organization.

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.

Chromatin ionic atmosphere analyzed by a mesoscale electrostatic approach

Characterizing the ionic distribution around chromatin is important for understanding the electrostatic forces governing chromatin structure and function. Here we develop an electrostatic model to handle multivalent ions and compute the ionic distribution around a mesoscale chromatin model as a function of conformation, number of nucleosome cores, and ionic strength and species using Poisson-Boltzmann theory. This approach enables us to visualize and measure the complex patterns of counterion condensation around chromatin by examining ionic densities, free energies, shielding charges, and correlations of shielding charges around the nucleosome core and various oligonucleosome conformations. We show that: counterions, especially divalent cations, predominantly condense around the nucleosomal and linker DNA, unburied regions of histone tails, and exposed chromatin surfaces; ionic screening is sensitively influenced by local and global conformations, with a wide ranging net nucleosome core screening charge (56-100e); and screening charge correlations reveal conformational flexibility and interactions among chromatin subunits, especially between the histone tails and parental nucleosome cores. These results provide complementary and detailed views of ionic effects on chromatin structure for modest computational resources. The electrostatic model developed here is applicable to other coarse-grained macromolecular complexes.

A structural perspective on the where, how, why, and what of nucleosome positioning

The DNA in eukaryotic chromatin is packed by histones into arrays of repeating units called nucleosomes. Each nucleosome contains a nucleosome core, where the DNA is wrapped around a histone octamer, and a stretch of relatively unconstrained DNA called the linker DNA. Since nucleosome cores occlude the DNA from many DNA-binding factors, their positions provide important clues for understanding chromatin packing and gene regulation. Here we review the recent advances in the genome-wide mapping of nucleosome positions, the molecular and structural determinants of nucleosome positioning, and the importance of nucleosome positioning in chromatin higher order folding and transcriptional regulation.