Table of contents

The histone-DNA interaction in the nucleosome is a fundamental mechanism of genomic compaction and regulation, which remains largely unknown despite increasing structural knowledge of the complex. In this paper, we propose a framework for the extraction of a nanoscale histone-DNA force-field from a collection of high-resolution structures, which may be adapted to a larger class of protein-DNA complexes. We applied the procedure to a large crystallographic database extended by snapshots from molecular dynamics simulations. The comparison of the structural models first shows that, at histone-DNA contact sites, the DNA base-pairs are shifted outwards locally, consistent with locally repulsive forces exerted by the histones. The second step shows that the various force profiles of the structures under analysis derive locally from a unique, sequence-independent, quadratic repulsive force-field, while the sequence preferences are entirely due to internal DNA mechanics. We have thus obtained the first knowledge-derived nanoscale interaction potential for histone-DNA in the nucleosome. The conformations obtained by relaxation of nucleosomal DNA with high-affinity sequences in this potential accurately reproduce the experimental values of binding preferences. Finally we address the more generic binding mechanisms relevant to the 80% genomic sequences incorporated in nucleosomes, by computing the conformation of nucleosomal DNA with sequence-averaged properties. This conformation differs from those found in crystals, and the analysis suggests that repulsive histone forces are related to local stretch tension in nucleosomal DNA, mostly between adjacent contact points. This tension could play a role in the stability of the complex.

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.

Chromatin, the structure in which DNA is compacted in eukaryotic cells, plays a key role in regulating DNA accessibility. FRET experiments on single nucleosomes, the basic units in chromatin, have revealed a dynamic nucleosome where spontaneous DNA unwrapping from the ends provides access to the nucleosomal DNA. Here we investigated how this DNA breathing is affected by extension of the linker DNA and by the presence of a neighboring nucleosome. We found that both electrostatic interactions between the entering and exiting linker DNA and nucleosome–nucleosome interactions increase unwrapping. Interactions between neighboring nucleosomes are more likely in dinucleosomes spaced by 55 bp of linker DNA than in dinucleosomes spaced by 50 bp of linker DNA. Such increased unwrapping may not only increase the accessibility of nucleosomal DNA in chromatin fibers, it may also be key to folding of nucleosomes into higher order structures.

Fluorescence resonance energy transfer (FRET) measurements allow one to observe site exposure in nucleosomes, i.e. the transient unwrapping of a part of the wrapped DNA from the histone octamer. In such experiments one can typically distinguish between a closed state and an open state but in principle one might hope to detect several states, each corresponding to a certain number of open binding sites. Here we show that even in an ideal FRET setup it would be hard to detect unwrapping states with intermediate levels of FRET efficiencies. As the unwrapped DNA molecule, modelled here as a wormlike chain, has a finite stiffness, shape fluctuations smear out FRET signals completely from such intermediate states.

Nucleosomes have to open to allow access to DNA in transcription, replication, and DNA damage repair. Changes in DNA torsional strain (e.g. during transcription elongation) influence the accessibility of nucleosomal DNA. Here we investigated the effect of DNA supercoiling-induced torsional strain on nucleosome structure and stability by scanning force microscopy (SFM) and fluorescence correlation spectroscopy (FCS). Nucleosomes were reconstituted onto 2.7 kb DNA plasmids with varying superhelical densities. The SFM results show a clear dependence of the amount of DNA wrapped around the nucleosome core on the strength and type of supercoiling. Negative supercoiling led to smaller nucleosome opening angles as compared to relaxed or positively supercoiled DNA. FCS experiments show that nucleosomes reconstituted on negatively superhelical DNA are more resistant to salt-induced destabilization, as seen by reduced H2A–H2B dimer eviction from the nucleosome. Our results show that changes in DNA topology, e.g. during transcription elongation, affect the accessibility of nucleosomal DNA.

DNA is known to condense with multivalent cations and positively charged proteins. However, the properties and energetics of DNA superstructures, such as chromatin, are poorly understood. As a model system, we investigate histone H1 condensation of DNA with tethered particle motion and force-extension measurements. We show that after the addition of H1 to DNA, a concentration dependent lag time is followed by the DNA spontaneously condensing. The trigger for this condensation phase transition can be modeled as sufficient H1s having bound to the DNA, providing insight into the 30 nm fiber condensation upon H1 binding. Furthermore, optical tweezers force-extension measurements of histone H1 condensed DNA reveals a sequence of state transitions corresponding to the unwinding of superhelical turns. We determine the complete, experimental, multi-state free energy landscape for the complex using Crooks fluctuation theorem. The measured force-versus-extension and free energy landscape are compared to predictions from a simple, theoretical model. This work encourages the theoretical description of DNA/protein structure and energetics and their role in chromatin and other, more complex, systems.

The multi-Cys₂His₂ (mC₂H₂) zinc finger protein, like CTCF, plays a central role in the three-dimensional organization of chromatin and gene regulation. The interaction between DNA and mC₂H₂ zinc finger proteins becomes crucial to better understand how CTCF dynamically shapes the chromatin structure. Here, we study a coarse-grained model of the mC₂H₂ zinc finger proteins in complexes with DNA, and in particular, we study how a mC₂H₂ zinc finger protein binds to and searches for its target DNA loci. On the basis of coarse-grained molecular dynamics simulations, we present several interesting kinetic conformational properties of the proteins, such as the rotation-coupled sliding, the asymmetrical roles of different zinc fingers and the partial binding partial dangling mode. In addition, two kinds of studied mC₂H₂ zinc finger proteins, of CG-rich and AT-rich binding motif each, were able to recognize their target sites and slide away from their non-target sites, which shows a proper sequence specificity in our model and the derived force field for mC₂H₂-DNA interaction. A further application to CTCF shows that the protein binds to a specific DNA duplex only with its central zinc fingers. The zinc finger domains of CTCF asymmetrically bend the DNA, but do not form a DNA loop alone in our simulations.

Recently, kinetic proofreading scenarios have been proposed for the regulation of chromatin remodeling, first on purely theoretical grounds (Blossey and Schiessel 2008 HFSP J.2 167–70) and deduced from experiments on the ISWI/ACF system (Narlikar 2010 Curr. Opin. Chem. Biol.14 660). In the kinetic proofreading scenario of chromatin remodeling, the combination of the recognition of a histone tail state and ATP-hydrolysis in the remodeler motor act together to select (i.e. proofread) a nucleosomal substrate. ISWI remodelers have recently been shown to have an additional level of regulation as they contain auto-inhibitory motifs which need to be inactivated through an interaction with the nucleosome. In this paper we show that the auto-regulatory effect enhances substrate recognition in kinetic proofreading. We further report some suggestive additional insights into the molecular mechanism underlying ISWI-autoregulation.

Gene regulation in eukaryotes requires the segregation of silenced genomic regions into densely packed heterochromatin, leaving the active genes in euchromatin regions more accessible. We introduce a model that connects the presence of epigenetically inherited histone marks, methylation at histone 3 lysine-9, to the physical compaction of chromatin fibers via the binding of heterochromatin protein 1 (HP1). Our model demonstrates some of the key physical features that are necessary to explain experimental observations. In particular, we demonstrate that strong cooperative interactions among the HP1 proteins are necessary to see the phase segregation of heterochromatin and euchromatin regions. We also explore how the cell can use the concentration of HP1 to control condensation and under what circumstances there is a threshold of methylation over which the fibers will compact. Finally, we consider how different potential in vivo fiber structures as well as the flexibility of the histone 3 tail can affect the bridging of HP1. Many of the observations that we make about the HP1 system are guided by general thermodynamics principles and thus could play a role in other DNA organizational processes such as the binding of linker histones.

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

The 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 (CoHex³⁺) 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 One8 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 CoHex³⁺. 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, spermidine³⁺.

The dynamic organization of chromatin plays an essential role in the regulation of gene expression and in other fundamental cellular processes. The underlying physical basis of these activities lies in the sequential positioning, chemical composition, and intermolecular interactions of the nucleosomes—the familiar assemblies of ∼150 DNA base pairs and eight histone proteins—found on chromatin fibers. Here we introduce a mesoscale model of short nucleosomal arrays and a computational framework that make it possible to incorporate detailed structural features of DNA and histones in simulations of short chromatin constructs. We explore the effects of nucleosome positioning and the presence or absence of cationic N-terminal histone tails on the 'local' inter-nucleosomal interactions and the global deformations of the simulated chains. The correspondence between the predicted and observed effects of nucleosome composition and numbers on the long-range communication between the ends of designed nucleosome arrays lends credence to the model and to the molecular insights gleaned from the simulated structures. We also extract effective nucleosome-nucleosome potentials from the simulations and implement the potentials in a larger-scale computational treatment of regularly repeating chromatin fibers. Our results reveal a remarkable effect of nucleosome spacing on chromatin flexibility, with small changes in DNA linker length significantly altering the interactions of nucleosomes and the dimensions of the fiber as a whole. In addition, we find that these changes in nucleosome positioning influence the statistical properties of long chromatin constructs. That is, simulated chromatin fibers with the same number of nucleosomes exhibit polymeric behaviors ranging from Gaussian to worm-like, depending upon nucleosome spacing. These findings suggest that the physical and mechanical properties of chromatin can span a wide range of behaviors, depending on nucleosome positioning, and that care must be taken in the choice of models used to interpret the experimental properties of long chromatin fibers.

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.

The notion of allostery introduced for proteins about fifty years ago has been extended since then to DNA allostery, where a locally triggered DNA structural transition remotely controls other DNA-binding events. We further extend this notion and propose that chromatin fiber allosteric transitions, induced by histone-tail covalent modifications, may play a key role in transcriptional regulation. We present an integrated scenario articulating allosteric mechanisms at different scales: allosteric transitions of the condensed chromatin fiber induced by histone-tail acetylation modify the mechanical constraints experienced by the embedded DNA, thus possibly controlling DNA-binding of allosteric transcription factors or further allosteric mechanisms at the linker DNA level. At a higher scale, different epigenetic constraints delineate different statistically dominant subsets of accessible chromatin fiber conformations, which each favors the assembly of dedicated regulatory complexes, as detailed on the emblematic example of the mouse Igf2-H19 gene locus and its parental imprinting. This physical view offers a mechanistic and spatially structured explanation of the observed correlation between transcriptional activity and histone modifications. The evolutionary origin of allosteric control supports to speak of an 'epigenetic code', by which events involved in transcriptional regulation are encoded in histone modifications in a context-dependent way.

The eukaryotic cell nucleus harbours the DNA genome that is organized in a dynamic chromatin network and embedded in a viscous crowded fluid. This environment directly affects enzymatic reactions and target search processes that access the DNA sequence information. However, its physical properties as a reaction medium are poorly understood. Here, we exploit mobility measurements of differently sized inert green fluorescent tracer proteins to characterize the viscoelastic properties of the nuclear interior of a living human cell. We find that it resembles a viscous fluid on small and large scales but appears viscoelastic on intermediate scales that change with protein size. Our results are consistent with simulations of diffusion through polymers and suggest that chromatin forms a random obstacle network rather than a self-similar structure with fixed fractal dimensions. By calculating how long molecules remember their previous position in dependence on their size, we evaluate how the nuclear environment affects search processes of chromatin targets.

Genetic information, which is stored in the long strand of genomic DNA as chromatin, must be scanned and read out by various transcription factors. First, gene-specific transcription factors, which are relatively small (∼50 kDa), scan the genome and bind regulatory elements. Such factors then recruit general transcription factors, Mediators, RNA polymerases, nucleosome remodellers, and histone modifiers, most of which are large protein complexes of 1–3 MDa in size. Here, we propose a new model for the functional significance of the size of transcription factors (or complexes) for gene regulation of chromatin domains. Recent findings suggest that chromatin consists of irregularly folded nucleosome fibres (10 nm fibres) and forms numerous condensed domains (e.g., topologically associating domains). Although the flexibility and dynamics of chromatin allow repositioning of genes within the condensed domains, the size exclusion effect of the domain may limit accessibility of DNA sequences by transcription factors. We used Monte Carlo computer simulations to determine the physical size limit of transcription factors that can enter condensed chromatin domains. Small gene-specific transcription factors can penetrate into the chromatin domains and search their target sequences, whereas large transcription complexes cannot enter the domain. Due to this property, once a large complex binds its target site via gene-specific factors it can act as a 'buoy' to keep the target region on the surface of the condensed domain and maintain transcriptional competency. This size-dependent specialization of target-scanning and surface-tethering functions could provide novel insight into the mechanisms of various DNA transactions, such as DNA replication and repair/recombination.

The dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in light of the recently developed Flory theory of untangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of the ring relaxation time and diffusion coefficient with ring length, as well as the time dependence of stress relaxation modulus, zero shear viscosity and the mean square averaged displacements of both individual monomers and the ring's mass centre. Our results agree within error bars with all available experimental and simulation data of the ring melt, although the quality of the data so far is insufficient to make a definitive judgement for or against the annealed tree theory. At the end we review briefly the relation between our findings and experimental data on chromatin dynamics.

We conduct Monte Carlo simulations to understand the spatial distribution of a polymer molecule confined within a rigid spherical capsule under crowding conditions, via a bead-spring chain model. To adjust the crowding level, the polymer is mixed with spherical crowders. As the interior of the capsule becomes more crowded, chain monomers tend to move to the capsule boundary under the penalty of conformational entropy. By incorporating some attraction between monomers and crowders, the polymer chain moves away from the capsule boundary. The interplay, between the conformational entropy, DNA-protein interaction, and molecular crowding induced depletion force between the chain and capsule boundary, may be essential to elucidate the heterogeneous chromatin structure in nuclei. Furthermore, the effects of chain length and size disparity between the monomers and the crowders are also investigated preliminarily.

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.

The estimation of contact probabilities (CP) from conformations of simulated bead-chain polymer models is a key step in methods that aim to elucidate the spatial organization of chromatin from analysis of experimentally determined contacts between different genomic loci. Although CPs can be estimated simply by counting contacts between beads in a sample of simulated chain conformations, reliable estimation of small CPs through this approach requires a large number of conformations, which can be computationally expensive to obtain. Here we describe an alternative computational method for estimating relatively small CPs without requiring large samples of chain conformations. In particular, we estimate the CPs from functional approximations to the cumulative distribution function (cdf) of the inter-bead distance for each pair of beads. These cdf approximations are obtained by fitting the extended generalized lambda distribution (EGLD) to inter-bead distances determined from a sample of chain conformations, which are in turn generated by Monte Carlo simulations. We find that CPs estimated from fitted EGLD cdfs are significantly more accurate than CPs estimated using contact counts from samples of limited size, and are more precise with all sample sizes, permitting as much as a tenfold reduction in conformation sample size for chains of 200 beads and samples smaller than 10⁵ conformations. This method of CP estimation thus has potential to accelerate computational efforts to elucidate the spatial organization of chromatin.