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

CG modeling of nucleosome arrays reveals the salt-dependent chromatin fiber conformational variability

Eukaryotic DNA is packaged in the cell nucleus into chromatin, composed of arrays of DNA-histone protein octamer complexes, the nucleosomes. Over the past decade, it has become clear that chromatin structure in vivo is not a hierarchy of well-organized folded nucleosome fibers but displays considerable conformational variability and heterogeneity. In vitro and in vivo studies, as well as computational modeling, have revealed that attractive nucleosome-nucleosome interaction with an essential role of nucleosome stacking defines chromatin compaction. The internal structure of compacted nucleosome arrays is regulated by the flexible and dynamic histone N-terminal tails. Since DNA is a highly negatively charged polyelectrolyte, electrostatic forces make a decisive contribution to chromatin formation and require the histones, particularly histone tails, to carry a significant positive charge. This also results in an essential role of mobile cations of the cytoplasm (K+, Na+, Mg2+) in regulating electrostatic interactions. Building on a previously successfully established bottom-up coarse-grained (CG) nucleosome model, we have developed a CG nucleosome array (chromatin fiber) model with the explicit presence of mobile ions and studied its conformational variability as a function of Na+ and Mg2+ ion concentration. With progressively elevated ion concentrations, we identified four main conformational states of nucleosome arrays characterized as extended, flexible, nucleosome-clutched, and globular fibers.

Combining molecular dynamics simulations and scoring method to computationally model ubiquitylated linker histones in chromatosomes

The chromatin in eukaryotic cells plays a fundamental role in all processes during a cell's life cycle. This nucleoprotein is normally tightly packed but needs to be unpacked for expression and division. The linker histones are critical for such packaging processes and while most experimental and simulation works recognize their crucial importance, the focus is nearly always set on the nucleosome as the basic chromatin building block. Linker histones can undergo several modifications, but only few studies on their ubiquitylation have been conducted. Mono-ubiquitylated linker histones (HUb), while poorly understood, are expected to influence DNA compaction. The size of ubiquitin and the globular domain of the linker histone are comparable and one would expect an increased disorder upon ubiquitylation of the linker histone. However, the formation of higher order chromatin is not hindered and ubiquitylation of the linker histone may even promote gene expression. Structural data on chromatosomes is rare and HUb has never been modeled in a chromatosome so far. Descriptions of the chromatin complex with HUb would greatly benefit from computational structural data. In this study we generate molecular dynamics simulation data for six differently linked HUb variants with the help of a sampling scheme tailored to drive the exploration of phase space. We identify conformational sub-states of the six HUb variants using the sketch-map algorithm for dimensionality reduction and iterative HDBSCAN for clustering on the excessively sampled, shallow free energy landscapes. We present a highly efficient geometric scoring method to identify sub-states of HUb that fit into the nucleosome. We predict HUb conformations inside a nucleosome using on-dyad and off-dyad chromatosome structures as reference and show that unbiased simulations of HUb produce significantly more fitting than non-fitting HUb conformations. A tetranucleosome array is used to show that ubiquitylation can even occur in chromatin without too much steric clashes.

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.

Biomolecular modeling thrives in the age of technology

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

Bottom-Up Coarse-Grained Modeling of DNA

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

The role of histone tails in nucleosome stability: An electrostatic perspective

We propose a methodology for the study of protein-DNA electrostatic interactions and apply it to clarify the effect of histone tails in nucleosomes. This method can be used to correlate electrostatic interactions to structural and functional features of protein-DNA systems, and can be combined with coarse-grained representations. In particular, we focus on the electrostatic field and resulting forces acting on the DNA. We investigate the electrostatic origins of effects such as different stages in DNA unwrapping, nucleosome destabilization upon histone tail truncation, and the role of specific arginines and lysines undergoing Post-Translational Modifications. We find that the positioning of the histone tails can oppose the attractive pull of the histone core, locally deform the DNA, and tune DNA unwrapping. Small conformational variations in the often overlooked H2A C-terminal tails had significant electrostatic repercussions near the DNA entry and exit sites. The H2A N-terminal tail exerts attractive electrostatic forces towards the histone core in positions where Polymerase II halts its progress. We validate our results with comparisons to previous experimental and computational observations.

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.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex³⁺). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex³⁺ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

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.

Bridging chromatin structure and function over a range of experimental spatial and temporal scales by molecular modeling

Chromatin structure, dynamics, and function are being intensely investigated by a variety of methods, including microscopy, X-ray diffraction, nuclear magnetic resonance, biochemical crosslinking, chromosome conformation capture, and computation. A range of experimental techniques combined with modeling is clearly valuable to help interpret experimental data and, importantly, generate configurations and mechanisms related to the 3D organization and function of the genome. Contact maps, in particular, as obtained by a variety of chromosome conformation capture methods, are of increasing interest due to their implications on genome structure and regulation on many levels. In this perspective, using seven examples from our group's studies, we illustrate how molecular modeling can help interpret such experimental data. Specifically, we show how computed contact maps related to experimental systems can be used to explain structures of nucleosomes, chromatin higher-order folding, domain segregation mechanisms, gene organization, and the effect on chromatin structure of external and internal fiber parameters, such as nucleosome positioning, presence of nucleosome free regions, histone posttranslational modifications, and linker histone binding. We argue that such computations on multiple spatial and temporal scales will be increasingly important for the integration of genomic, epigenomic, and biophysical data on chromatin structure and related cellular processes.

Large-scale simulations of nucleoprotein complexes: ribosomes, nucleosomes, chromatin, chromosomes and CRISPR

Recent advances in biotechnology such as Hi-C, CRISPR/Cas9 and ribosome display have placed nucleoprotein complexes at center stage. Understanding the structural dynamics of these complexes aids in optimizing protocols and interpreting data for these new technologies. The integration of simulation and experiment has helped advance mechanistic understanding of these systems. Coarse-grained simulations, reduced-description models, and explicit solvent molecular dynamics simulations yield useful complementary perspectives on nucleoprotein complex structural dynamics. When combined with Hi-C, cryo-EM, and single molecule measurements, these simulations integrate disparate forms of experimental data into a coherent mechanism.

Nucleosome Crowding in Chromatin Slows the Diffusion but Can Promote Target Search of Proteins

Dynamics of nuclear proteins in crowded chromatin has only been poorly understood. Here, we address the diffusion, target search, and structural dynamics of three proteins in a model chromatin using coarse-grained molecular simulations run on the K computer. We prepared two structures of chromatin made of 20 nucleosomes with different nucleosome densities and investigated dynamics of two transcription factors, HMGB1 and p53, and one signaling protein, ERK, embedded in the chromatin. We found fast and normal diffusion of the nuclear proteins in the low-density chromatins and slow and subdiffusional movements in the high-density chromatin. The diffusion of the largest transcription factor, p53, is slowed by high-density chromatin most markedly. The on rates and off rates for DNA binding are increased and decreased, respectively, in the high-density chromatin. To our surprise, the DNA sequence search was faster in chromatin with high nucleosome density, though the diffusion is slower. We also found that the three nuclear proteins preferred to bind on the linker DNA and the entry and exit regions of nucleosomal DNA. In addition to these regions, HMGB1 and p53 also bound to the dyad.

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

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

The effect of linker DNA on the structure and interaction of nucleosome core particles

In eukaryotes, the compaction of chromatin fibers composed of nucleosome core particles (NCPs) connected by a linker DNA into chromosomes is highly efficient; however, the underlying folding mechanisms remain elusive. We used small angle X-ray scattering (SAXS) to investigate the influence of linker DNA length on the local structure and the interparticle interactions of the NCPs. In the presence of the linker DNA of 30 bp or less in length, the results suggest partial unwrapping of nucleosomal DNA on the NCP irrespective of the linker DNA length. Moreover, the presence of 15 bp linker DNA alleviated the electrostatic repulsion between the NCPs and prevented the formation of an ordered columnar hexagonal phase, demonstrating that the linker DNA plays an active role in chromatin folding.

General method for rapid purification of native chromatin fragments

Biochemical, proteomic, and epigenetic studies of chromatin rely on the ability to efficiently isolate native nucleosomes in high yield and purity. However, isolation of native chromatin suitable for many downstream experiments remains a challenging task. This is especially true for the budding yeast Saccharomyces cerevisiae, which continues to serve as an important model organism for the study of chromatin structure and function. Here, we developed a time- and cost-efficient universal protocol for isolation of native chromatin fragments from yeast, insect, and mammalian cells. The resulting protocol preserves histone posttranslational modification in the native chromatin state and is applicable for both parallel multisample spin-column purification and large-scale isolation. This protocol is based on the efficient and stable purification of polynucleosomes and features a combination of optimized cell lysis and purification conditions, three options for chromatin fragmentation, and a novel ion-exchange chromatographic purification strategy. The procedure will aid chromatin researchers interested in isolating native chromatin material for biochemical studies and serve as a mild, acid- and detergent-free sample preparation method for MS analysis.

Force-extension behavior of DNA in the presence of DNA-bending nucleoid associated proteins

Interactions between nucleoid associated proteins (NAPs) and DNA affect DNA polymer conformation, leading to phenomena such as concentration dependent force-extension behavior. These effects, in turn, also impact the local binding behavior of the protein, such as high forces causing proteins to unbind, or proteins binding favorably to locally bent DNA. We develop a coarse-grained NAP-DNA simulation model that incorporates both force- and concentration-dependent behaviors, in order to study the interplay between NAP binding and DNA conformation. This model system includes multi-state protein binding and unbinding, motivated by prior work, but is now dependent on the local structure of the DNA, which is related to external forces acting on the DNA strand. We observe the expected qualitative binding behavior, where more proteins are bound at lower forces than at higher forces. Our model also includes NAP-induced DNA bending, which affects DNA elasticity. We see semi-quantitative matching of our simulated force-extension behavior to the reported experimental data. By using a coarse-grained simulation, we are also able to look at non-equilibrium behaviors, such as dynamic extension of a DNA strand. We stretch a DNA strand at different rates and at different NAP concentrations to observe how the time scales of the system (such as pulling time and unbinding time) work in concert. When these time scales are similar, we observe measurable rate-dependent changes in the system, which include the number of proteins bound and the force required to extend the DNA molecule. This suggests that the relative time scales of different dynamic processes play an important role in the behavior of NAP-DNA systems.

A systematic analysis of nucleosome core particle and nucleosome-nucleosome stacking structure

Chromatin condensation is driven by the energetically favourable interaction between nucleosome core particles (NCPs). The close NCP-NCP contact, stacking, is a primary structural element of all condensed states of chromatin in vitro and in vivo. However, the molecular structure of stacked nucleosomes as well as the nature of the interactions involved in its formation have not yet been systematically studied. Here we undertake an investigation of both the structural and physico-chemical features of NCP structure and the NCP-NCP stacking. We introduce an “NCP-centred” set of parameters (NCP-NCP distance, shift, rise, tilt, and others) that allows numerical characterisation of the mutual positions of the NCPs in the stacking and in any other structures formed by the NCP. NCP stacking in more than 140 published NCP crystal structures were analysed. In addition, coarse grained (CG) MD simulations modelling NCP condensation was carried out. The CG model takes into account details of the nucleosome structure and adequately describes the long range electrostatic forces as well as excluded volume effects acting in chromatin. The CG simulations showed good agreement with experimental data and revealed the importance of the H2A and H4 N-terminal tail bridging and screening as well as tail-tail correlations in the stacked nucleosomes.

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.

The Influence of Ionic Environment and Histone Tails on Columnar Order of Nucleosome Core Particles

The nucleosome core particle (NCP) is the basic building block of chromatin. Nucleosome-nucleosome interactions are instrumental in chromatin compaction, and understanding NCP self-assembly is important for understanding chromatin structure and dynamics. Recombinant NCPs aggregated by multivalent cations form various ordered phases that can be studied by x-ray diffraction (small-angle x-ray scattering). In this work, the effects on the supramolecular structure of aggregated NCPs due to lysine histone H4 tail acetylations, histone H2A mutations (neutralizing the acidic patch of the histone octamer), and the removal of histone tails were investigated. The formation of ordered mainly hexagonal columnar NCP phases is in agreement with earlier studies; however, the highly homogeneous recombinant NCP systems used in this work display a more compact packing. The long-range order of the NCP columnar phase was found to be abolished or reduced by acetylation of the H4 tails, acidic patch neutralization, and removal of the H3 and H2B tails. Loss of nucleosome stacking upon removal of the H3 tails in combination with other tails was observed. In the absence of the H2A tails, the formation of an unknown highly ordered phase was observed.

A Molecular View of the Dynamics of dsDNA Packing Inside Viral Capsids in the Presence of Ions

Genome packing in viruses and prokaryotes relies on positively charged ions to reduce electrostatic repulsions, and induce attractions that can facilitate DNA condensation. Here we present molecular dynamics simulations spanning several microseconds of dsDNA packing inside nanometer-sized viral capsids. We use a detailed molecular model of DNA that accounts for molecular structure, basepairing, and explicit counterions. The size and shape of the capsids studied here are based on the 30-nanometer-diameter gene transfer agents of bacterium Rhodobacter capsulatus that transfer random 4.5-kbp (1.5 μm) DNA segments between bacterial cells. Multivalent cations such as spermidine and magnesium induce attraction between packaged DNA sites that can lead to DNA condensation. At high concentrations of spermidine, this condensation significantly increases the shear stresses on the packaged DNA while also reducing the pressure inside the capsid. These effects result in an increase in the packing velocity and the total amount of DNA that can be packaged inside the nanometer-sized capsids. In the simulation results presented here, high concentrations of spermidine³⁺ did not produce the premature stalling observed in experiments. However, a small increase in the heterogeneity of packing velocities was observed in the systems with magnesium and spermidine ions compared to the system with only salt. The results presented here indicate that the effect of multivalent cations and of spermidine, in particular, on the dynamics of DNA packing, increases with decreasing packing velocities.

Multiscale coarse-grained modelling of chromatin components: DNA and the nucleosome

To model large biomolecular systems, such as cell and organelles an atomistic description is not currently achievable and is not generally practical. Therefore, simplified coarse-grained (CG) modelling becomes a necessity. One of the most important cellular components is chromatin, a large DNA-protein complex where DNA is highly compacted. Recent progress in coarse graining modelling of the major chromatin components, double helical DNA and the nucleosome core particle (NCP) is presented. First, general principles and approaches allowing rigorous bottom-to-top generation of interaction potentials in the CG models are presented. Then, recent CG models of DNA are reviewed and their adequacy is benchmarked against experimental data on the salt dependence of DNA flexibility (persistence length). Furthermore, a few recent CG models of the NCP are described and their application for studying salt-dependent NCP-NCP interaction is discussed. An example of a multiscale approach to CG modelling of chromatin is presented where interactions and self-assembly of thousands of NCPs in solution are observed.

Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

Coarse-Grained Ions for Nucleic Acid Modeling

We present a general coarse-grained model of sodium, magnesium, spermidine, and chlorine in implicit solvent. The effective potentials between ions are systematically parametrized using a relative entropy coarse-graining approach [Carmichael, S. P. and M. S. Shell, J. Phys. Chem. B, 116, 8383-93 (2012)] that maximizes the information retained in a coarse-grained model. We describe the local distribution of ions in the vicinity of a recently published coarse-grained DNA model and demonstrate a dependence of persistence length on ionic strength that differs from that predicted by Odijk-Skolnick-Fixman theory. Consistent with experimental observations, we show that spermidine induces DNA condensation whereas magnesium and sodium do not. This model can be used alongside any coarse-grained DNA model that has explicit charges and an accurate reproduction of the excluded volume of dsDNA.

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.

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.

Multiscale modelling of nucleosome core particle aggregation

The nucleosome core particle (NCP) is the basic building block of chromatin. Under the influence of multivalent cations, isolated mononucleosomes exhibit a rich phase behaviour forming various columnar phases with characteristic NCP-NCP stacking. NCP stacking is also a regular element of chromatin structure in vivo. Understanding the mechanism of nucleosome stacking and the conditions leading to self-assembly of NCPs is still incomplete. Due to the complexity of the system and the need to describe electrostatics properly by including the explicit mobile ions, novel modelling approaches based on coarse-grained (CG) methods at the multiscale level becomes a necessity. In this work we present a multiscale CG computer simulation approach to modelling interactions and self-assembly of solutions of NCPs induced by the presence of multivalent cations. Starting from continuum simulations including explicit three-valent cobalt(III)hexammine (CoHex(3+)) counterions and 20 NCPs, based on a previously developed advanced CG NCP model with one bead per amino acid and five beads per two DNA base pair unit (Fan et al 2013 PLoS One 8 e54228), we use the inverse Monte Carlo method to calculate effective interaction potentials for a 'super-CG' NCP model consisting of seven beads for each NCP. These interaction potentials are used in large-scale simulations of up to 5000 NCPs, modelling self-assembly induced by CoHex(3+). The systems of 'super-CG' NCPs form a single large cluster of stacked NCPs without long-range order in agreement with experimental data for NCPs precipitated by the three-valent polyamine, spermidine(3+).

A simple model for DNA bridging proteins and bacterial or human genomes: bridging-induced attraction and genome compaction

We present computer simulations of the phase behaviour of an ensemble of proteins interacting with a polymer, mimicking non-specific binding to a piece of bacterial DNA or eukaryotic chromatin. The proteins can simultaneously bind to the polymer in two or more places to create protein bridges. Despite the lack of any explicit interaction between the proteins or between DNA segments, our simulations confirm previous results showing that when the protein-polymer interaction is sufficiently strong, the proteins come together to form clusters. Furthermore, a sufficiently large concentration of bridging proteins leads to the compaction of the swollen polymer into a globular phase. Here we characterise both the formation of protein clusters and the polymer collapse as a function of protein concentration, protein-polymer affinity and fibre flexibility.

Close encounters with DNA

Over the past ten years, the all-atom molecular dynamics method has grown in the scale of both systems and processes amenable to it and in its ability to make quantitative predictions about the behavior of experimental systems. The field of computational DNA research is no exception, witnessing a dramatic increase in the size of systems simulated with atomic resolution, the duration of individual simulations and the realism of the simulation outcomes. In this topical review, we describe the hallmark physical properties of DNA from the perspective of all-atom simulations. We demonstrate the amazing ability of such simulations to reveal the microscopic physical origins of experimentally observed phenomena. We also discuss the frustrating limitations associated with imperfections of present atomic force fields and inadequate sampling. The review is focused on the following four physical properties of DNA: effective electric charge, response to an external mechanical force, interaction with other DNA molecules and behavior in an external electric field.

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.