Mesoscale simulations of two nucleosome-repeat length oligonucleosomes

Structure of native chromatin fibres revealed by Cryo-ET in situ

The structure of chromatin plays pivotal roles in regulating gene transcription, DNA replication and repair, and chromosome segregation. This structure, however, remains elusive. Here, using cryo-FIB and cryo-ET, we delineate the 3D architecture of native chromatin fibres in intact interphase human T-lymphoblasts and determine the in situ structures of nucleosomes in different conformations. These chromatin fibres are not structured as uniform 30 nm one-start or two-start filaments but are composed of relaxed, variable zigzag organizations of nucleosomes connected by straight linker DNA. Nucleosomes with little H1 and linker DNA density are distributed randomly without any spatial preference. This work will inspire future high-resolution investigations on native chromatin structures in situ at both a single-nucleosome level and a population level under many different cellular conditions in health and disease.

Brownian dynamics simulations of mesoscale chromatin fibers

The relationship between chromatin architecture and function defines a central problem in biology and medicine. Many computational chromatin models with atomic, coarse-grained, mesoscale, and polymer resolution have been used to shed light onto the mechanisms that dictate genome folding and regulation of gene expression. The associated simulation techniques range from Monte Carlo to molecular, Brownian, and Langevin dynamics. Here, we present an efficient Compute Unified Device Architecture (CUDA) implementation of Brownian dynamics (BD) to simulate chromatin fibers at the nucleosome resolution with our chromatin mesoscale model. With the CUDA implementation for computer architectures with graphic processing units (GPUs), we significantly accelerate compute-intensive hydrodynamic tensor calculations in the BD simulations by massive parallelization, boosting the performance a hundred-fold compared with central processing unit calculations. We validate our BD simulation approach by reproducing experimental trends on fiber diffusion and structure as a function of salt, linker histone binding, and histone-tail composition, as well as Monte Carlo equilibrium sampling results. Our approach proves to be physically accurate with performance that makes feasible the study of chromatin fibers in the range of kb or hundreds of nucleosomes (small gene). Such simulations are essential to advance the study of biological processes such as gene regulation and aberrant genome-structure related diseases.

Histone tails cooperate to control the breathing of genomic nucleosomes

Genomic DNA is packaged in chromatin, a dynamic fiber variable in size and compaction. In chromatin, repeating nucleosome units wrap 145–147 DNA basepairs around histone proteins. Genetic and epigenetic regulation of genes relies on structural transitions in chromatin which are driven by intra- and inter-nucleosome dynamics and modulated by chemical modifications of the unstructured terminal tails of histones. Here we demonstrate how the interplay between histone H3 and H2A tails control ample nucleosome breathing motions. We monitored large openings of two genomic nucleosomes, and only moderate breathing of an engineered nucleosome in atomistic molecular simulations amounting to 24 μs. Transitions between open and closed nucleosome conformations were mediated by the displacement and changes in compaction of the two histone tails. These motions involved changes in the DNA interaction profiles of clusters of epigenetic regulatory aminoacids in the tails. Removing the histone tails resulted in a large increase of the amplitude of nucleosome breathing but did not change the sequence dependent pattern of the motions. Histone tail modulated nucleosome breathing is a key mechanism of chromatin dynamics with important implications for epigenetic regulation.

In the cell, the DNA is packed in chromatin. Chromatin is a highly dynamic fiber structure made of arrays of nucleosomes with different degrees of compaction. Each nucleosome has 145–147 basepairs of DNA wrapped around a protein octamer made of four unique histone proteins. Each histone is present twice and has a structured part and one or two disordered terminal tails. The regulation of gene expression in the cell and during cellular transitions depends on dynamic changes in chromatin structure. Chromatin dynamics are modulated by intra and inter nucleosome motions and by posttranslational chemical modifications of the histone tails. Here we reveal how histone tails control the intra nucleosome dynamics at atomic resolution. From extensive sampling of nucleosome dynamics in atomistic molecular simulations, we show that genomic nucleosomes breath more extensively than engineered ones and we describe how two histone tails cooperate to control nucleosome breathing through interactions between clusters of positively charged residues and the DNA. Nucleosome conformations with different degrees of opening are associated with different conformations, positions, and DNA interaction patterns of the tails. With this mechanism, we contribute to the understanding of chromatin dynamics at atomic resolution.

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.

Entropic effect of macromolecular crowding enhances binding between nucleosome clutches in heterochromatin, but not in euchromatin

Sharp increase in macromolecular crowding induces abnormal chromatin compaction in the cell nucleus, suggesting its non-negligible impact on chromatin structure and function. However, the details of the crowding-induced chromatin compaction remain poorly understood. In this work, we present a computer simulation study on the entropic effect of macromolecular crowding on the interaction between chromatin structural units called nucleosome clutches. Nucleosome clutches were modeled by a chain of nucleosomes collapsed by harmonic restraints implicitly mimicking the nucleosome association mediated by histone tails and linker histones. The nucleosome density of the clutches was set close to either that of high-density heterochromatin or that of low-density euchromatin. The effective interactions between these nucleosome clutches were calculated in various crowding conditions, and it was found that the increase in the degree of macromolecular crowding induced attractive interaction between two clutches with high nucleosome density. Interestingly, the increased degree of macromolecular crowding did not induce any attraction between two clutches with low nucleosome density. Our results suggest that the entropic effect of macromolecular crowding can enhance binding between nucleosome clutches in heterochromatin, but not in euchromatin, as a result of the difference in nucleosome packing degrees.

Dependence of the Linker Histone and Chromatin Condensation on the Nucleosome Environment

The linker histone (LH), an auxiliary protein that can bind to chromatin and interact with the linker DNA to form stem motifs, is a key element of chromatin compaction. By affecting the chromatin condensation level, it also plays an active role in gene expression. However, the presence and variable concentration of LH in chromatin fibers with different DNA linker lengths indicate that its folding and condensation are highly adaptable and dependent on the immediate nucleosome environment. Recent experimental studies revealed that the behavior of LH in mononucleosomes markedly differs from that in small nucleosome arrays, but the associated mechanism is unknown. Here we report a structural analysis of the behavior of LH in mononucleosomes and oligonucleosomes (2-6 nucleosomes) using mesoscale chromatin simulations. We show that the adapted stem configuration heavily depends on the strength of electrostatic interactions between LH and its parental DNA linkers, and that those interactions tend to be asymmetric in small oligonucleosome systems. Namely, LH in oligonucleosomes dominantly interacts with one DNA linker only, as opposed to mononucleosomes where LH has similar interactions with both linkers and forms a highly stable nucleosome stem. Although we show that the LH condensation depends sensitively on the electrostatic interactions with entering and exiting DNA linkers, other interactions, especially by nonparental cores and nonparental linkers, modulate the structural condensation by softening LH and thus making oligonucleosomes more flexible, in comparison to to mono- and dinucleosomes. We also find that the overall LH/chromatin interactions sensitively depend on the linker length because the linker length determines the maximal nucleosome stem length. For mononucleosomes with DNA linkers shorter than LH, LH condenses fully, while for DNA linkers comparable or longer than LH, the LH extension in mononucleosomes strongly follows the length of DNA linkers, unhampered by neighboring linker histones. Thus, LH is more condensed for mononucleosomes with short linkers, compared to oligonucleosomes, and its orientation is variable and highly environment-dependent. More generally, the work underscores the agility of LH whose folding dynamics critically controls genomic packaging and gene expression.

Confinement-driven organization of a histone-complexed DNA molecule in a dense array of nanoposts

The first step in the controlled storage of lengthy DNA molecules is to keep DNA molecules separated while integrated in micrometer-sized space. Herein, we present hybrid Monte Carlo simulations of a histone-complexed DNA (hcDNA) molecule confined in a dense array of nanoposts. Depending on the nanopost dimension, a single, 8.7 kilobase pair hcDNA molecule was either localized and elongated in a single inter-post space surrounded by four nanoposts or spread over several inter-post spaces through passages between two neighboring nanoposts. The conformational change of a hcDNA molecule is interpreted in terms of competitive effects of confinements in the inter-post and passage spaces. We propose that, by elaborately designing nanopost arrays, the competitive confinement effects can be adjusted such that each hcDNA molecule is localized in a single inter-post space, and thereby multiple hcDNA molecules can be physically separated from each other while stored together in the nanopost array.

Linking Chromatin Fibers to Gene Folding by Hierarchical Looping

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

Mesoscale Modeling Reveals Hierarchical Looping of Chromatin Fibers Near Gene Regulatory Elements

While it is well-recognized that chromatin loops play an important role in gene regulation, structural details regarding higher order chromatin loops are only emerging. Here we present a systematic study of restrained chromatin loops ranging from 25 to 427 nucleosomes (fibers of 5-80 Kb DNA in length), mimicking gene elements studied by 3C contact data. We find that hierarchical looping represents a stable configuration that can effectively bring distant regions of the GATA-4 gene together, satisfying connections reported by 3C experiments. Additionally, we find that restrained chromatin fibers larger than 100 nucleosomes (∼20Kb) form closed plectonemes, whereas fibers shorter than 100 nucleosomes form simple hairpin loops. By studying the dependence of loop structures on internal parameters, we show that loop features are sensitive to linker histone concentration, loop length, divalent ions, and DNA linker length. Specifically, increasing loop length, linker histone concentration, and divalent ion concentration are associated with increased persistence length (or decreased bending), while varying DNA linker length in a manner similar to experimentally observed "nucleosome free regions" (found near transcription start sites) disrupts intertwining and leads to loop opening and increased persistence length in linker histone depleted (-LH) fibers. Chromatin fiber structure sensitivity to these parameters, all of which vary throughout the cell cycle, tissue type, and species, suggests that caution is warranted when using uniform polymer models to fit chromatin conformation capture genome-wide data. Furthermore, the folding geometry we observe near the transcription initiation site of the GATA-4 gene suggests that hierarchical looping provides a structural mechanism for gene inhibition, and offers tunable parameters for design of gene regulation elements.

Correlation among DNA Linker Length, Linker Histone Concentration, and Histone Tails in Chromatin

Eukaryotic cells condense their genetic material in the nucleus in the form of chromatin, a macromolecular complex made of DNA and multiple proteins. The structure of chromatin is intimately connected to the regulation of all eukaryotic organisms, from amoebas to humans, but its organization remains largely unknown. The nucleosome repeat length (NRL) and the concentration of linker histones (ρLH) are two structural parameters that vary among cell types and cell cycles; the NRL is the number of DNA basepairs wound around each nucleosome core plus the number of basepairs linking successive nucleosomes. Recent studies have found a linear empirical relationship between the variation of these two properties for different cells, but its underlying mechanism remains elusive. Here we apply our established mesoscale chromatin model to explore the mechanisms responsible for this relationship, by investigating chromatin fibers as a function of NRL and ρLH combinations. We find that a threshold of linker histone concentration triggers the compaction of chromatin into well-formed 30-nm fibers; this critical value increases linearly with NRL, except for long NRLs, where the fibers remain disorganized. Remarkably, the interaction patterns between core histone tails and chromatin elements are highly sensitive to the NRL and ρLH combination, suggesting a molecular mechanism that could have a key role in regulating the structural state of the fibers in the cell. An estimate of the minimized work and volume associated with storage of chromatin fibers in the nucleus further suggests factors that could spontaneously regulate the NRL as a function of linker histone concentration. Both the tail interaction map and DNA packing considerations support the empirical NRL/ρLH relationship and offer a framework to interpret experiments for different chromatin conditions in the cell.

Searching target sites on DNA by proteins: Role of DNA dynamics under confinement

DNA-binding proteins (DBPs) rapidly search and specifically bind to their target sites on genomic DNA in order to trigger many cellular regulatory processes. It has been suggested that the facilitation of search dynamics is achieved by combining 3D diffusion with one-dimensional sliding and hopping dynamics of interacting proteins. Although, recent studies have advanced the knowledge of molecular determinants that affect one-dimensional search efficiency, the role of DNA molecule is poorly understood. In this study, by using coarse-grained simulations, we propose that dynamics of DNA molecule and its degree of confinement due to cellular crowding concertedly regulate its groove geometry and modulate the inter-communication with DBPs. Under weak confinement, DNA dynamics promotes many short, rotation-decoupled sliding events interspersed by hopping dynamics. While this results in faster 1D diffusion, associated probability of missing targets by jumping over them increases. In contrast, strong confinement favours rotation-coupled sliding to locate targets but lacks structural flexibility to achieve desired specificity. By testing under physiological crowding, our study provides a plausible mechanism on how DNA molecule may help in maintaining an optimal balance between fast hopping and rotation-coupled sliding dynamics, to locate target sites rapidly and form specific complexes precisely.

A simple biophysical model emulates budding yeast chromosome condensation

Mitotic chromosomes were one of the first cell biological structures to be described, yet their molecular architecture remains poorly understood. We have devised a simple biophysical model of a 300 kb-long nucleosome chain, the size of a budding yeast chromosome, constrained by interactions between binding sites of the chromosomal condensin complex, a key component of interphase and mitotic chromosomes. Comparisons of computational and experimental (4C) interaction maps, and other biophysical features, allow us to predict a mode of condensin action. Stochastic condensin-mediated pairwise interactions along the nucleosome chain generate native-like chromosome features and recapitulate chromosome compaction and individualization during mitotic condensation. Higher order interactions between condensin binding sites explain the data less well. Our results suggest that basic assumptions about chromatin behavior go a long way to explain chromosome architecture and are able to generate a molecular model of what the inside of a chromosome is likely to look like.

Forced unraveling of chromatin fibers with nonuniform linker DNA lengths

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

Search by proteins for their DNA target site: 1. The effect of DNA conformation on protein sliding

The recognition of DNA-binding proteins (DBPs) to their specific site often precedes by a search technique in which proteins slide, hop along the DNA contour or perform inter-segment transfer and 3D diffusion to dissociate and re-associate to distant DNA sites. In this study, we demonstrated that the strength and nature of the non-specific electrostatic interactions, which govern the search dynamics of DBPs, are strongly correlated with the conformation of the DNA. We tuned two structural parameters, namely curvature and the extent of helical twisting in circular DNA. These two factors are mutually independent of each other and can modulate the electrostatic potential through changing the geometry of the circular DNA conformation. The search dynamics for DBPs on circular DNA is therefore markedly different compared with linear B-DNA. Our results suggest that, for a given DBP, the rotation-coupled sliding dynamics is precluded in highly curved DNA (as well as for over-twisted DNA) because of the large electrostatic energy barrier between the inside and outside of the DNA molecule. Under such circumstances, proteins prefer to hop in order to explore interior DNA sites. The change in the balance between sliding and hopping propensities as a function of DNA curvature or twisting may result in different search efficiency and speed.

Monte-Carlo simulations of PAMAM dendrimer-DNA interactions

We use Monte Carlo simulations to determine the influence of poly(amido amine) (PAMAM) dendrimer size and charge on its interactions with double-stranded DNA conformation and interaction strength. To achieve a compromise between simulation speed and molecular detail, we combine the coarse-grained DNA model of de Pablo et al. which resolves each DNA base using three beads - and thereby retains the double-helix structure - with a dendrimer model with resolution similar to that of the DNA. The resulting predictions of the effects of dendrimer generation, dendrimer surface charge density, and salt concentration on dendrimer-DNA complexes are in agreement with both experiments and all-atom MD simulations. The model predicts that DNA wraps a fully charged G5 or G6 dendrimer at low salt concentration (10 mM) similarly to a histone octamer, and for the G5 dendrimer, DNA super helices with both handednesses occur. At salt concentrations above 50 mM, or when a high fraction of dendrimer surface charges are neutralized by acetylation, DNA adheres but does not compactly wrap the dendrimer, in agreement with experimental findings. We are also able to simulate pairs of dendrimers binding to the same DNA strand. Thus, our mesoscale simulation not only elucidates dendrimer-DNA interactions, but also provides a methodology for efficiently simulating chromatin formation and other cationic macroion-DNA complexes.

Dynamic condensation of linker histone C-terminal domain regulates chromatin structure

The basic and intrinsically disordered C-terminal domain (CTD) of the linker histone (LH) is essential for chromatin compaction. However, its conformation upon nucleosome binding and its impact on chromatin organization remain unknown. Our mesoscale chromatin model with a flexible LH CTD captures a dynamic, salt-dependent condensation mechanism driven by charge neutralization between the LH and linker DNA. Namely, at low salt concentration, CTD condenses, but LH only interacts with the nucleosome and one linker DNA, resulting in a semi-open nucleosome configuration; at higher salt, LH interacts with the nucleosome and two linker DNAs, promoting stem formation and chromatin compaction. CTD charge reduction unfolds the domain and decondenses chromatin, a mechanism in consonance with reduced counterion screening in vitro and phosphorylated LH in vivo. Divalent ions counteract this decondensation effect by maintaining nucleosome stems and expelling the CTDs to the fiber exterior. Additionally, we explain that the CTD folding depends on the chromatin fiber size, and we show that the asymmetric structure of the LH globular head is responsible for the uneven interaction observed between the LH and the linker DNAs. All these mechanisms may impact epigenetic regulation and higher levels of chromatin folding.

Structure-driven homology pairing of chromatin fibers: the role of electrostatics and protein-induced bridging

Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.

Effect of capsid confinement on the chromatin organization of the SV40 minichromosome

Using small-angle X-ray scattering, we determined the three-dimensional packing architecture of the minichromosome confined within the SV40 virus. In solution, the minichromosome, composed of closed circular dsDNA complexed in nucleosomes, was shown to be structurally similar to cellular chromatin. In contrast, we find a unique organization of the nanometrically encapsidated chromatin, whereby minichromosomal density is somewhat higher at the center of the capsid and decreases towards the walls. This organization is in excellent agreement with a coarse-grained computer model, accounting for tethered nucleosomal interactions under viral capsid confinement. With analogy to confined liquid crystals, but contrary to the solenoid structure of cellular chromatin, our simulations indicate that the nucleosomes within the capsid lack orientational order. Nucleosomes in the layer adjacent to the capsid wall, however, align with the boundary, thereby inducing a 'molten droplet' state of the chromatin. These findings indicate that nucleosomal interactions suffice to predict the genome organization in polyomavirus capsids and underscore the adaptable nature of the eukaryotic chromatin architecture to nanoscale confinement.

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

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

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

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

Modelling chromatin structure and dynamics: status and prospects

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

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.

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.

Nucleosome distribution and linker DNA: connecting nuclear function to dynamic chromatin structure

Genetic information in eukaryotes is managed by strategic hierarchical organization of chromatin structure. Primary chromatin structure describes an unfolded nucleosomal array, often referred to as "beads on a string". Chromatin is compacted by the nonlinear rearrangement of nucleosomes to form stable secondary chromatin structures. Chromatin conformational transitions between primary and secondary structures are mediated by both nucleosome-stacking interactions and the intervening linker DNA. Chromatin model system studies find that the topography of secondary structures is sensitive to the spacing of nucleosomes within an array. Understanding the relationship between nucleosome spacing and higher order chromatin structure will likely yield important insights into the dynamic nature of secondary chromatin structure as it occurs in vivo. Genome-wide nucleosome mapping studies find the distance between nucleosomes varies, and regions of uniformly spaced nucleosomes are often interrupted by regions of nonuniform spacing. This type of organization is found at a subset of actively transcribed genes in which a nucleosome-depleted region near the transcription start site is directly adjacent to uniformly spaced nucleosomes in the coding region. Here, we evaluate secondary chromatin structure and discuss the structural and functional implications of variable nucleosome distributions in different organisms and at gene regulatory junctions.

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.

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.

Modeling studies of chromatin fiber structure as a function of DNA linker length

Chromatin fibers encountered in various species and tissues are characterized by different nucleosome repeat lengths (NRLs) of the linker DNA connecting the nucleosomes. While single cellular organisms and rapidly growing cells with high protein production have short NRL ranging from 160 to 189 bp, mature cells usually have longer NRLs ranging between 190 and 220 bp. Recently, various experimental studies have examined the effect of NRL on the internal organization of chromatin fiber. Here, we investigate by mesoscale modeling of oligonucleosomes the folding patterns for different NRL, with and without linker histone (LH), under typical monovalent salt conditions using both one-start solenoid and two-start zigzag starting configurations. We find that short to medium NRL chromatin fibers (173 to 209 bp) with LH condense into zigzag structures and that solenoid-like features are viable only for longer NRLs (226 bp). We suggest that medium NRLs are more advantageous for packing and various levels of chromatin compaction throughout the cell cycle than their shortest and longest brethren; the former (short NRLs) fold into narrow fibers, while the latter (long NRLs) arrays do not easily lead to high packing ratios due to possible linker DNA bending. Moreover, we show that the LH has a small effect on the condensation of short-NRL arrays but has an important condensation effect on medium-NRL arrays, which have linker lengths similar to the LH lengths. Finally, we suggest that the medium-NRL species, with densely packed fiber arrangements, may be advantageous for epigenetic control because their histone tail modifications can have a greater effect compared to other fibers due to their more extensive nucleosome interaction network.

Biomolecular Structure and Modeling: Problem and Application Perspective

The experimental progress described in the previous chapter has been accompanied by an increasing desire to relate the complex three-dimensional (3D) shapes of biomolecules to their biological functions and interactions with other molecular systems. Structural biology, computational biology, genomics, proteomics, bioinformatics, chemoinformatics, and others are natural partner disciplines in such endeavors.

Protein Structure Hierarchy

The complexity of protein structures requires a description of their structural components. This chapter describes the elements of protein secondary structure — regular local structural patterns — such as helices, sheets, turns, and loops. Helices and sheets tend to fall into specific regions in the {ϕ, ψ} space of the Ramachandran plot (see Figures 28 and 29). The corresponding width and shape of each region reflects the spread of that motif as found in proteins.