Nucleosome repositioning via loop formation

Sequence Dependence in Nucleosome Dynamics

The basic packaging unit of eukaryotic chromatin is the nucleosome that contains 145-147 base pair duplex DNA wrapped around an octameric histone protein. While the DNA sequence plays a crucial role in controlling the positioning of the nucleosome, the molecular details behind the interplay between DNA sequence and nucleosome dynamics remain relatively unexplored. This study analyzes this interplay in detail by performing all-atom molecular dynamics simulations of nucleosomes, comparing the human α-satellite palindromic (ASP) and the strong positioning "Widom-601" DNA sequence at time scales of 12 μs. The simulations are performed at salt concentrations 10-20 times higher than physiological salt concentrations to screen the electrostatic interactions and promote unwrapping. These microsecond-long simulations give insight into the molecular-level sequence-dependent events that dictate the pathway of DNA unwrapping. We find that the "ASP" sequence forms a loop around SHL ± 5 for three sets of simulations. Coincident with loop formation is a cooperative increase in contacts with the neighboring N-terminal H2B tail and C-terminal H2A tail and the release of neighboring counterions. We find that the Widom-601 sequence exhibits a strong breathing motion of the nucleic acid ends. Coincident with the breathing motion is the collapse of the full N-terminal H3 tail and formation of an α-helix that interacts with the H3 histone core. We postulate that the dynamics of these histone tails and their modification with post-translational modifications (PTMs) may play a key role in governing this dynamics.

The role of transcript regions and amino acid choice in nucleosome positioning

Eukaryotic DNA is organized and compacted in a string of nucleosomes, DNA-wrapped protein cylinders. The positions of nucleosomes along DNA are not random but show well-known base pair sequence preferences that result from the sequence-dependent elastic and geometric properties of the DNA double helix. Here, we focus on DNA around transcription start sites, which are known to typically attract nucleosomes in multicellular life forms through their high GC content. We aim to understand how these GC signals, as observed in genome-wide averages, are produced and encoded through different genomic regions (mainly 5' UTRs, coding exons, and introns). Our study uses a bioinformatics approach to decompose the genome-wide GC signal into between-region and within-region signals. We find large differences in GC signal contributions between vertebrates and plants and, remarkably, even between closely related species. Introns contribute most to the GC signal in vertebrates, while in plants the exons dominate. Further, we find signal strengths stronger on DNA than on mRNA, suggesting a biological function of GC signals along the DNA itself, as is the case for nucleosome positioning. Finally, we make the surprising discovery that both the choice of synonymous codons and amino acids contribute to the nucleosome positioning signal.

Multiplexing mechanical and translational cues on genes

The genetic code gives precise instructions on how to translate codons into amino acids. Due to the degeneracy of the genetic code-18 out of 20 amino acids are encoded for by more than one codon-more information can be stored in a basepair sequence. Indeed, various types of additional information have been discussed in the literature, e.g., the positioning of nucleosomes along eukaryotic genomes and the modulation of the translating efficiency in ribosomes to influence cotranslational protein folding. The purpose of this study is to show that it is indeed possible to carry more than one additional layer of information on top of a gene. In particular, we show how much translation efficiency and nucleosome positioning can be adjusted simultaneously without changing the encoded protein. We achieve this by mapping genes on weighted graphs that contain all synonymous genes, and then finding shortest paths through these graphs. This enables us, for example, to readjust the disrupted translational efficiency profile after a gene has been introduced from one organism (e.g., human) into another (e.g., yeast) without greatly changing the nucleosome landscape intrinsically encoded by the DNA molecule.

Visualizing Conformational Ensembles of the Nucleosome by NMR

The formation of chromatin not only compacts the eukaryotic genome into the nucleus but also provides a mechanism for the regulation of all DNA templated processes. Spatial and temporal modulation of the chromatin structure is critical in such regulation and involves fine-tuned functioning of the basic subunit of chromatin, the nucleosome. It has become apparent that the nucleosome is an inherently dynamic system, but characterization of these dynamics at the atomic level has remained challenging. NMR spectroscopy is a powerful tool for investigating the conformational ensemble and dynamics of proteins and protein complexes, and recent advances have made the study of large systems possible. Here, we review recent studies which utilize NMR spectroscopy to uncover the atomic level conformation and dynamics of the nucleosome and provide a better understanding of the importance of these dynamics in key regulatory events.

Translational nucleosome positioning: A computational study

About three-quarters of eukaryotic DNA is wrapped into nucleosomes; DNA spools with a protein core. The affinity of a given DNA stretch to be incorporated into a nucleosome is known to depend on the base-pair sequence-dependent geometry and elasticity of the DNA double helix. This causes the rotational and translational positioning of nucleosomes. In this study we ask the question whether the latter can be predicted by a simple coarse-grained DNA model with sequence-dependent elasticity, the rigid base-pair model. Whereas this model is known to be rather robust in predicting rotational nucleosome positioning, we show that the translational positioning is a rather subtle effect that is dominated by the guanine-cytosine content dependence of entropy rather than energy. A correct qualitative prediction within the rigid base-pair framework can only be achieved by assuming that DNA elasticity effectively changes on complexation into the nucleosome complex. With that extra assumption we arrive at a model which gives an excellent quantitative agreement to experimental in vitro nucleosome maps, under the additional assumption that nucleosomes equilibrate their positions only locally.

Ensembles of Breathing Nucleosomes: A Computational Study

About three-fourths of the human DNA molecules are wrapped into nucleosomes, protein spools with DNA. Nucleosomes are highly dynamic, transiently exposing their DNA through spontaneous unspooling. Recent experiments allowed to observe the DNA of an ensemble of such breathing nucleosomes through x-ray diffraction with contrast matching between the solvent and the protein core. In this study, we calculate such an ensemble through a Monte Carlo simulation of a coarse-grained nucleosome model with sequence-dependent DNA mechanics. Our analysis gives detailed insights into the sequence dependence of nucleosome breathing observed in the experiment and allows us to determine the adsorption energy of the DNA bound to the protein core as a function of the ionic strength. Moreover, we predict the breathing behavior of other potentially interesting sequences and compare the findings to earlier related experiments.

Twist-bend coupling, twist waves, and the shape of DNA loops

By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100 base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape that reproduces the exact loop energy up to the fourth significant digit and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.

Nanoscale dynamics of centromere nucleosomes and the critical roles of CENP-A

In the absence of a functioning centromere, chromosome segregation becomes aberrant, leading to an increased rate of aneuploidy. The highly specific recognition of centromeres by kinetochores suggests that specific structural characteristics define this region, however, the structural details and mechanism underlying this recognition remains a matter of intense investigation. To address this, high-speed atomic force microscopy was used for direct visualization of the spontaneous dynamics of CENP-A nucleosomes at the sub-second time scale. We report that CENP-A nucleosomes change conformation spontaneously and reversibly, utilizing two major pathways: unwrapping, and looping of the DNA; enabling core transfer between neighboring DNA substrates. Along with these nucleosome dynamics we observed that CENP-A stabilizes the histone core against dissociating to histone subunits upon unwrapping DNA, unique from H3 cores which are only capable of such plasticity in the presence of remodeling factors. These findings have implications for the dynamics and integrity of nucleosomes at the centromere.

Theory of Site-Specific DNA-Protein Interactions in the Presence of Nucleosome Roadblocks

We show that nucleosomes exert a maximal amount of hindrance to the one-dimensional diffusion of transcription factors (TFs) when they are present between TFs and their cognate sites on DNA. The effective one-dimensional diffusion coefficient of TFs (χ_TF) decreases with a rise in the free-energy barrier (μ_NU) of the sliding of nucleosomes as χ_TF∝exp(-μ_NU). The average time (η_L) required by TFs to slide over L sites on DNA increases with μ_NU as η_L∝exp(μ_NU). When TFs move close to nucleosomes, then they exhibit typical subdiffusion. Nucleosomes can enhance the search dynamics of TFs when TFs are present between nucleosomes and TF binding sites. These results suggest that nucleosome-depleted regions around the cognate sites of TFs are mandatory for efficient site-specific binding of TFs. Remarkably, the genome-wide in vivo positioning pattern of TFs shows a maximum at their specific binding sites where the occupancy of nucleosomes shows a minimum. This could be a consequence of an increasing level of breathing dynamics of nucleosome cores and decreasing levels of fluctuations in the DNA binding domains of TFs as they move across TF binding sites. The dynamics of TFs becomes slow as they approach their cognate sites so that TFs form a tight site-specific complex, whereas the dynamics of nucleosomes becomes rapid so that they quickly pass through the cognate sites of TFs. Several in vivo data sets on the genome-wide positioning pattern of nucleosomes and TFs agree well with our arguments. The retarding effects of nucleosomes can be minimized when the degree of condensation of DNA is such that it can permit a jump size associated with the dynamics of TFs beyond ∼160-180 bp.

The base pair-scale diffusion of nucleosomes modulates binding of transcription factors

The structure of promoter chromatin determines the ability of transcription factors (TFs) to bind to DNA and therefore has a profound effect on the expression levels of genes. However, the role of spontaneous nucleosome movements in this process is not fully understood. Here, we developed a single-molecule optical tweezers assay capable of simultaneously characterizing the base pair-scale diffusion of a nucleosome on DNA and the binding of a TF, using the luteinizing hormone β subunit gene (Lhb) promoter and Egr-1 as a model system. Our results demonstrate that nucleosomes undergo confined diffusion, and that the incorporation of the histone variant H2A.Z serves to partially relieve this confinement, inducing a different type of nucleosome repositioning. The increase in diffusion leads to exposure of a TF's binding site and facilitates its association with the DNA, which, in turn, biases the subsequent movement of the nucleosome. Our findings suggest the use of mobile nucleosomes as a general transcriptional regulatory mechanism.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.

Shortest paths through synonymous genomes

The elasticity of the DNA double helix varies with the underlying base pair sequence. This allows one to put mechanical cues into sequences that in turn influence the packaging of DNA into nucleosomes, DNA-wrapped protein cylinders. Nucleosomes dictate a broad range of biological processes, ranging from gene regulation, recombination, and replication to chromosome condensation. Here we map base pair sequences onto graphs and use shortest paths algorithms to determine which DNA stretches are easiest or hardest to bend inside a nucleosome. We further demonstrate how genetic and mechanical information can be multiplexed by studying paths through graphs of synonymous codons. Using this method we find that nucleosomes can be placed by mechanical cues nearly everywhere on the genome of baker's yeast (Saccharomyces cerevisiae).

Defect-facilitated buckling in supercoiled double-helix DNA

We present a statistical-mechanical model for stretched twisted double-helix DNA, where thermal fluctuations are treated explicitly from a Hamiltonian without using any scaling hypotheses. Our model applied to defect-free supercoiled DNA describes the coexistence of multiple plectoneme domains in long DNA molecules at physiological salt concentrations (≈0.1M Na^{+}) and stretching forces (≈1pN). We find a higher (lower) number of domains at lower (higher) ionic strengths and stretching forces, in accord with experimental observations. We use our model to study the effect of an immobile point defect on the DNA contour that allows a localized kink. The degree of the kink is controlled by the defect size, such that a larger defect further reduces the bending energy of the defect-facilitated kinked end loop. We find that a defect can spatially pin a plectoneme domain via nucleation of a kinked end loop, in accord with experiments and simulations. Our model explains previously reported magnetic tweezer experiments [A. Dittmore et al., Phys. Rev. Lett. 119, 147801 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.147801] showing two buckling signatures: buckling and "rebuckling" in supercoiled DNA with a base-unpaired region. Comparing with experiments, we find that under 1 pN force, a kinked end loop nucleated at a base-mismatched site reduces the bending energy by ≈0.7 k_{B}T per unpaired base. Our model predicts the coexistence of three states at the buckling and rebuckling transitions, which warrants new experiments.

Nucleation of Multiple Buckled Structures in Intertwined DNA Double Helices

We study the statistical-mechanical properties of intertwined double-helical DNAs (DNA braids). In magnetic tweezers experiments, we find that torsionally stressed stretched braids supercoil via an abrupt buckling transition, which is associated with the nucleation of a braid end loop, and that the buckled braid is characterized by a proliferation of multiple domains. Differences between the mechanics of DNA braids and supercoiled single DNAs can be understood as an effect of the increased bulkiness in the structure of the former. The experimental results are in accord with the predictions of a statistical-mechanical model.

In silico evidence for sequence-dependent nucleosome sliding

Nucleosomes represent the basic building block of chromatin and provide an important mechanism by which cellular processes are controlled. The locations of nucleosomes across the genome are not random but instead depend on both the underlying DNA sequence and the dynamic action of other proteins within the nucleus. These processes are central to cellular function, and the molecular details of the interplay between DNA sequence and nucleosome dynamics remain poorly understood. In this work, we investigate this interplay in detail by relying on a molecular model, which permits development of a comprehensive picture of the underlying free energy surfaces and the corresponding dynamics of nucleosome repositioning. The mechanism of nucleosome repositioning is shown to be strongly linked to DNA sequence and directly related to the binding energy of a given DNA sequence to the histone core. It is also demonstrated that chromatin remodelers can override DNA-sequence preferences by exerting torque, and the histone H4 tail is then identified as a key component by which DNA-sequence, histone modifications, and chromatin remodelers could in fact be coupled.

Transcription dynamics stabilizes nucleus-like layer structure in chromatin brush

We use a brush of DNA in a solution of transcriptional machinery and histone proteins to theoretically predict that this brush shows phase separation due to the instability arising from the disassembly of nucleosomes during transcription. In the two-phase coexistent state, collapsed chains (with relatively large nucleosome occupancy) lie at the grafting surface and swollen chains (with relatively small nucleosome occupancy) are distributed at the space above the collapsed chains, analogous to the structure of chromatin in differentiated cells. This layer structure is stabilized by the lateral osmotic pressure of swollen chains. For a relatively small grafting density, DNA brushes show tricritical points because the entropic elasticity with respect to the lateral excursion of swollen chains balances with the lateral osmotic pressure of these chains. At the tricritical points, DNA brushes show large fluctuations of local nucleosome concentration, which may be reminiscent of the fluctuations observed in embryonic stem cells.

Torque and buckling in stretched intertwined double-helix DNAs

We present a statistical-mechanical model for the behavior of intertwined DNAs, with a focus on their torque and extension as a function of their catenation (linking) number and applied force, as studied in magnetic tweezers experiments. Our model produces results in good agreement with available experimental data and predicts a catenation-dependent effective twist modulus distinct from what is observed for twisted individual double-helix DNAs. We find that buckling occurs near the point where experiments have observed a kink in the extension versus linking number, and that the subsequent "supercoiled braid" state corresponds to a proliferation of multiple small plectoneme structures. We predict a discontinuity in extension at the buckling transition corresponding to nucleation of the first plectoneme domain. We also find that buckling occurs for lower linking number at lower salt; the opposite trend is observed for supercoiled single DNAs.

Nucleosome mobility and the regulation of gene expression: Insights from single-molecule studies

Nucleosomes at the promoters of genes regulate the accessibility of the transcription machinery to DNA, and function as a basic layer in the complex regulation of gene expression. Our understanding of the role of the nucleosome's spontaneous, thermally driven position changes in modulating expression is lacking. This is the result of the paucity of experimental data on these dynamics, at high-resolution, and for DNA sequences that belong to real, transcribed genes. We have developed an assay that uses partial, reversible unzipping of nucleosomes with optical tweezers to repeatedly probe a nucleosome's position over time. Using the nucleosomes at the promoters of two model genes, Cga and Lhb, we show that the mobility of nucleosomes is modulated by the sequence of DNA and by the use of alternative histone variants, and describe how the mobility can affect transcription, at the initiation and elongation phases.

Extra views on structure and dynamics of DNA loops on nucleosomes studied with molecular simulations

It has been shown experimentally that the action of the RSC chromatin remodeler leads to the formation of an irregular, partially remodeled nucleosome, termed a remosome. The remosome contains an extra 30-40 base pairs of DNA compared to a canonical nucleosome. Large-scale molecular simulations have provided information on the probable structure of remosomes and have explained why they remain stable in the absence of RSC. Here we explain how these simulations were carried out and what the resulting remosome models imply in terms of the mechanism of action of RSC. We notably show that local kinks within DNA are key in explaining how extra DNA can be in added to nucleosomes without unduly disturbing DNA-histone binding.

Structure and dynamics of DNA loops on nucleosomes studied with atomistic, microsecond-scale molecular dynamics

DNA loop formation on nucleosomes is strongly implicated in chromatin remodeling and occurs spontaneously in nucleosomes subjected to superhelical stress. The nature of such loops depends crucially on the balance between DNA deformation and DNA interaction with the nucleosome core. Currently, no high-resolution structural data on these loops exist. Although uniform rod models have been used to study loop size and shape, these models make assumptions concerning DNA mechanics and DNA-core binding. We present here atomic-scale molecular dynamics simulations for two different loop sizes. The results point to the key role of localized DNA kinking within the loops. Kinks enable the relaxation of DNA bending strain to be coupled with improved DNA-core interactions. Kinks lead to small, irregularly shaped loops that are asymmetrically positioned with respect to the nucleosome core. We also find that loop position can influence the dynamics of the DNA segments at the extremities of the nucleosome.

Nucleosome dynamics: Sequence matters

About three quarter of all eukaryotic DNA is wrapped around protein cylinders, forming nucleosomes. Even though the histone proteins that make up the core of nucleosomes are highly conserved in evolution, nucleosomes can be very different from each other due to posttranslational modifications of the histones. Another crucial factor in making nucleosomes unique has so far been underappreciated: the sequence of their DNA. This review provides an overview of the experimental and theoretical progress that increasingly points to the importance of the nucleosomal base pair sequence. Specifically, we discuss the role of the underlying base pair sequence in nucleosome positioning, sliding, breathing, force-induced unwrapping, dissociation and partial assembly and also how the sequence can influence higher-order structures. A new view emerges: the physical properties of nucleosomes, especially their dynamical properties, are determined to a large extent by the mechanical properties of their DNA, which in turn depends on DNA sequence.

Transcription Driven Phase Separation in Chromatin Brush

We theoretically predict the local density of nucleosomes on DNA brushes in a solution of molecules, which are necessary for transcription and the assembly of nucleosomes. Our theory predicts that in a confined space, DNA brushes show phase separation, where a region of relatively large nucleosomal occupancy coexists with a region of smaller nucleosomal occupancy. This phase separation is driven by an instability arising from the fact that the rate of transcription increases as the nucleosomal occupancy decreases due to the excluded volume interactions between nucleosomes and RNA polymerase during thermal diffusion and, in turn, nucleosomes are (in some cases) desorbed from DNA when RNA polymerase collides with nucleosomes during transcription. The miscibility phase diagram shows critical points, which are sensitive to the rate constants involved in transcription, the changes of interactions of DNA chain segments by assembling nucleosomes, and pressures that are applied to the brushes.

Genome-wide profiling of nucleosome sensitivity and chromatin accessibility in Drosophila melanogaster

Nucleosomal DNA is thought to be generally inaccessible to DNA-binding factors, such as micrococcal nuclease (MNase). Here, we digest Drosophila chromatin with high and low concentrations of MNase to reveal two distinct nucleosome types: MNase-sensitive and MNase-resistant. MNase-resistant nucleosomes assemble on sequences depleted of A/T and enriched in G/C-containing dinucleotides, whereas MNase-sensitive nucleosomes form on A/T-rich sequences found at transcription start and termination sites, enhancers and DNase I hypersensitive sites. Estimates of nucleosome formation energies indicate that MNase-sensitive nucleosomes tend to be less stable than MNase-resistant ones. Strikingly, a decrease in cell growth temperature of about 10°C makes MNase-sensitive nucleosomes less accessible, suggesting that observed variations in MNase sensitivity are related to either thermal fluctuations of chromatin fibers or the activity of enzymatic machinery. In the vicinity of active genes and DNase I hypersensitive sites nucleosomes are organized into periodic arrays, likely due to 'phasing' off potential barriers formed by DNA-bound factors or by nucleosomes anchored to their positions through external interactions. The latter idea is substantiated by our biophysical model of nucleosome positioning and energetics, which predicts that nucleosomes immediately downstream of transcription start sites are anchored and recapitulates nucleosome phasing at active genes significantly better than sequence-dependent models.

Computational study of remodeling in a nucleosomal array

Chromatin remodeling complexes utilize the energy of ATP hydrolysis to change the packing state of chromatin, e.g. by catalysing the sliding of nucleosomes along DNA. Here we present simple models to describe experimental data of changes in DNA accessibility along a synthetic, repetitive array of nucleosomes during remodeling by the ACF enzyme or its isolated ATPase subunit, ISWI. We find substantial qualitative differences between the remodeling activities of ISWI and ACF. To understand better the observed behavior for the ACF remodeler, we study more microscopic models of nucleosomal arrays.

Fokker-Planck description of single nucleosome repositioning by dimeric chromatin remodelers

Recent experiments have demonstrated that the ATP-utilizing chromatin assembly and remodeling factor (ACF) is a dimeric, processive motor complex which can move a nucleosome more efficiently towards longer flanking DNA than towards shorter flanking DNA strands, thereby centering an initially ill-positioned nucleosome on DNA substrates. We give a Fokker-Planck description for the repositioning process driven by transitions between internal chemical states of the remodelers. In the chemical states of ATP hydrolysis during which the repositioning takes place a power stroke is considered. The slope of the effective driving potential is directly related to ATP hydrolysis and leads to the unidirectional motion of the nucleosome-remodeler complex along the DNA strand. The Einstein force relation allows us to deduce the ATP-concentration dependence of the diffusion constant of the nucleosome-remodeler complex. We have employed our model to study the efficiency of positioning of nucleosomes as a function of the ATP sampling rate between the two motors which shows that the synchronization between the motors is crucial for the remodeling mechanism to work.

ISWI remodelers slide nucleosomes with coordinated multi-base-pair entry steps and single-base-pair exit steps

ISWI-family enzymes remodel chromatin by sliding nucleosomes along DNA, but the nucleosome translocation mechanism remains unclear. Here we use single-molecule FRET to probe nucleosome translocation by ISWI-family remodelers. Distinct ISWI-family members translocate nucleosomes with a similar stepping pattern maintained by the catalytic subunit of the enzyme. Nucleosome remodeling begins with a 7 bp step of DNA translocation followed by 3 bp subsequent steps toward the exit side of nucleosomes. These multi-bp, compound steps are comprised of 1 bp substeps. DNA movement on the entry side of the nucleosome occurs only after 7 bp of exit-side translocation, and each entry-side step draws in a 3 bp equivalent of DNA that allows three additional base pairs to be moved to the exit side. Our results suggest a remodeling mechanism with well-defined coordination at different nucleosomal sites featuring DNA translocation toward the exit side in 1 bp steps preceding multi-bp steps of DNA movement on the entry side.

Sequence-based prediction of single nucleosome positioning and genome-wide nucleosome occupancy

Nucleosome positioning dictates eukaryotic DNA compaction and access. To predict nucleosome positions in a statistical mechanics model, we exploited the knowledge that nucleosomes favor DNA sequences with specific periodically occurring dinucleotides. Our model is the first to capture both dyad position within a few base pairs, and free binding energy within 2 k(B)T, for all the known nucleosome positioning sequences. By applying Percus's equation to the derived energy landscape, we isolate sequence effects on genome-wide nucleosome occupancy from other factors that may influence nucleosome positioning. For both in vitro and in vivo systems, three parameters suffice to predict nucleosome occupancy with correlation coefficients of respectively 0.74 and 0.66. As predicted, we find the largest deviations in vivo around transcription start sites. This relatively simple algorithm can be used to guide future studies on the influence of DNA sequence on chromatin organization.

Footprint traversal by adenosine-triphosphate-dependent chromatin remodeler motor

Adenosine-triphosphate (ATP)-dependent chromatin remodeling enzymes (CREs) are biomolecular motors in eukaryotic cells. These are driven by a chemical fuel, namely, ATP. CREs actively participate in many cellular processes that require accessibility of specific segments of DNA which are packaged as chromatin. The basic unit of chromatin is a nucleosome where 146 bp ∼ 50 nm of a double-stranded DNA (dsDNA) is wrapped around a spool formed by histone proteins. The helical path of histone-DNA contact on a nucleosome is also called "footprint." We investigate the mechanism of footprint traversal by a CRE that translocates along the dsDNA. Our two-state model of a CRE captures effectively two distinct chemical (or conformational) states in the mechanochemical cycle of each ATP-dependent CRE. We calculate the mean time of traversal. Our predictions on the ATP dependence of the mean traversal time can be tested by carrying out in vitro experiments on mononucleosomes.

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

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

SSB functions as a sliding platform that migrates on DNA via reptation

SSB proteins bind to and control the accessibility of single-stranded DNA (ssDNA), likely facilitated by their ability to diffuse on ssDNA. Using a hybrid single-molecule method combining fluorescence and force, we probed how proteins with large binding site sizes can migrate rapidly on DNA and how protein-protein interactions and tension may modulate the motion. We observed force-induced progressive unraveling of ssDNA from the SSB surface between 1 and 6 pN, followed by SSB dissociation at ∼10 pN, and obtained experimental evidence of a reptation mechanism for protein movement along DNA wherein a protein slides via DNA bulge formation and propagation. SSB diffusion persists even when bound with RecO and at forces under which the fully wrapped state is perturbed, suggesting that even in crowded cellular conditions SSB can act as a sliding platform to recruit and carry its interacting proteins for use in DNA replication, recombination and repair.

The dynamics of the nucleosome: thermal effects, external forces and ATP

With nucleosomes being tightly associated with the majority of eukaryotic DNA, it is essential that mechanisms are in place that can move nucleosomes 'out of the way'. A focus of current research comprises chromatin remodeling complexes, which are ATP-consuming protein complexes that, for example, pull or push nucleosomes along DNA. The precise mechanisms used by those complexes are not yet understood. Hints for possible mechanisms might be found among the various spontaneous fluctuations that nucleosomes show in the absence of remodelers. Thermal fluctuations induce the partial unwrapping of DNA from the nucleosomes and introduce twist or loop defects in the wrapped DNA, leading to nucleosome sliding along DNA. In this minireview, we discuss nucleosome dynamics from two angles. First, we describe the dynamical modes of nucleosomes in the absence of remodelers that are experimentally fairly well characterized and theoretically understood. Then, we discuss remodelers and describe recent insights about the possible schemes that they might use.

SWI/SNF- and RSC-catalyzed nucleosome mobilization requires internal DNA loop translocation within nucleosomes

The multisubunit SWI/SNF and RSC complexes utilize energy derived from ATP hydrolysis to mobilize nucleosomes and render the DNA accessible for various nuclear processes. Here we test the idea that remodeling involves intermediates with mobile DNA bulges or loops within the nucleosome by cross-linking the H2A N- or C-terminal tails together to generate protein "loops" that constrict separation of the DNA from the histone surface. Analyses indicate that this intranucleosomal cross-linking causes little or no change in remodeling-dependent exposure of DNA sequences within the nucleosome to restriction enzymes. However, cross-linking inhibits nucleosome mobilization and blocks complete movement of nucleosomes to extreme end positions on the DNA fragments. These results are consistent with evidence that nucleosome remodeling involves intermediates with DNA loops on the nucleosome surface but indicate that such loops do not freely diffuse about the surface of the histone octamer. We propose a threading model for movement of DNA loops around the perimeter of the nucleosome core.

Salt-modulated structure of polyelectrolyte-macroion complex fibers

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5-6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.

Conformation and mechanical properties of closed diblock fibers

We analyze the conformations and mechanical properties of closed diblock fibers. In our model, the length fraction of each component and the total fiber length are controlled by tunable chemical potentials. Our formalism can describe fibers in which one block is a bare polymer while the other is an adsorbed protein-filament complex; these blocks maintain different bending rigidities and spontaneous curvatures. We analytically calculate the shape of two-component polymers for all values of the material parameters and chemical potentials. Our results yield a complete analytical description of all possible two-component polymer conformations, a phase portrait detailing the parameter spaces in which these shapes occur, and the identification of spontaneous transitions between shapes driven by environmental changes.

Dynamics of loop formation in a semiflexible polymer

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical and experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study [K. P. Santo and K. L. Sebastian, Phys. Rev. E 73, 031923 (2006)], we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We make use of the "closure approximation" of Wilemski and Fixman [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 878 (1974)], in which a sink function is used to represent the reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain. We show that for short chains, the loop formation time tau decreases with the contour length of the polymer. But for longer chains, it increases with length obeying a power law and so it has a minimum at an intermediate length. In terms of dimensionless variables, the closing time is found to be given by tau approximately Ln exp(const/L), where n=4.5-6. The minimum loop formation time occurs at a length Lm of about 2.2-2.4. These are, indeed, the results that are physically expected, but a multidimensional analysis leading to these results does not seem to exist in the literature so far.

Chromatin remodeling in silico: a stochastic model for SWI/SNF

Beside their contribution in DNA packaging, histone-core particles modulate the transcription machinery access to the DNA through dynamic chromatin structure. Chromatin remodeling complexes perturb such modulations through diverse mechanisms. SWI/SNF is a well-studied highly conserved chromatin remodeling complex that is ubiquitous across eukaryotes. Rigorous study of experimental observations suggests randomness in dynamics of SWI/SNF in cis chromatin remodeling process. In this work we propose a stochastic computational model that captures such fluctuations. We incorporate the physiological properties of the process through parametric microevents. Each microevent is then associated with a stochastic model that couples its random temporal and spatial dynamics with the energy landscape of the remodeling process. We further show that DNA sequence stacks and friction force have negligible effect on chromatin remodeling. Our approach shows a promising approximation to the force impinged on the DNA by the SWI/SNF complex. We validate our model predictions with several experimental data sets. The proposed model suggest that the in cis translocation rate of histone-core particle follows a Gamma distribution. By carefully analyzing the simulation results we conjecture that SWI/SNF chromatin remodeling has low energy efficiency (<0.30). We use our model to recapitulate the dynamics of the parallel remodeling processes that occur in close proximity across a typical eukaryotic genome. Our results suggest that the orchestrated chromatin remodeling makes few kilobase-pairs of the DNA accessible to the transcription machinery in a timely manner.

Nucleosome disassembly intermediates characterized by single-molecule FRET

The nucleosome has a central role in the compaction of genomic DNA and the control of DNA accessibility for transcription and replication. To help understanding the mechanism of nucleosome opening and closing in these processes, we studied the disassembly of mononucleosomes by quantitative single-molecule FRET with high spatial resolution, using the SELEX-generated "Widom 601" positioning sequence labeled with donor and acceptor fluorophores. Reversible dissociation was induced by increasing NaCl concentration. At least 3 species with different FRET were identified and assigned to structures: (i) the most stable high-FRET species corresponding to the intact nucleosome, (ii) a less stable mid-FRET species that we attribute to a first intermediate with a partially unwrapped DNA and less histones, and (iii) a low-FRET species characterized by a very broad FRET distribution, representing highly unwrapped structures and free DNA formed at the expense of the other 2 species. Selective FCS analysis indicates that even in the low-FRET state, some histones are still bound to the DNA. The interdye distance of 54.0 A measured for the high-FRET species corresponds to a compact conformation close to the known crystallographic structure. The coexistence and interconversion of these species is first demonstrated under non-invasive conditions. A geometric model of the DNA unwinding predicts the presence of the observed FRET species. The different structures of these species in the disassembly pathway map the energy landscape indicating major barriers for 10-bp and minor ones for 5-bp DNA unwinding steps.

Active nucleosome displacement: a theoretical approach

Three-quarters of eukaryotic DNA are wrapped around protein cylinders forming so-called nucleosomes that block the access to the genetic information. Nucleosomes need therefore to be repositioned, either passively (by thermal fluctuations) or actively (by molecular motors). Here we introduce a theoretical model that allows us to study the interplay between a motor protein that moves along DNA (e.g., an RNA polymerase) and a nucleosome that it encounters on its way. We aim at describing the displacement mechanisms of the nucleosome and the motor protein on a microscopic level to understand better the intricate interplay between the active step of the motor and the nucleosome-repositioning step. Different motor types (Brownian ratchet versus power-stroke mechanism) that perform very similarly under a constant load are shown to have very different nucleosome repositioning capacities.

DNA sequence-directed organization of chromatin: structure-based computational analysis of nucleosome-binding sequences

The folding of DNA on the nucleosome core particle governs many fundamental issues in eukaryotic molecular biology. In this study, an updated set of sequence-dependent empirical "energy" functions, derived from the structures of other protein-bound DNA molecules, is used to investigate the extent to which the architecture of nucleosomal DNA is dictated by its underlying sequence. The potentials are used to estimate the cost of deforming a collection of sequences known to bind or resist uptake in nucleosomes along various left-handed superhelical pathways and to deduce the features of sequence contributing to a particular structural form. The deformation scores reflect the choice of template, the deviations of structural parameters at each step of the nucleosome-bound DNA from their intrinsic values, and the sequence-dependent "deformability" of a given dimer. The correspondence between the computed scores and binding propensities points to a subtle interplay between DNA sequence and nucleosomal folding, e.g., sequences with periodically spaced pyrimidine-purine steps deform at low cost along a kinked template whereas sequences that resist deformation prefer a smoother spatial pathway. Successful prediction of the known settings of some of the best-resolved nucleosome-positioning sequences, however, requires a template with "kink-and-slide" steps like those found in high-resolution nucleosome structures.

Stochastic model for nucleosome sliding under an external force

Heat-induced diffusion of nucleosomes along DNA is an experimentally well-studied phenomenon, presumably induced by twist defects that propagate through the wrapped DNA portion. The diffusion constant depends dramatically on the local mechanical properties of the DNA and the presence of DNA-binding ligands. This has been quantitatively understood by a stochastic three-state model. Future experiments are expected to allow application of forces on the nucleosome that induce a directed sliding. By extending the three-state model, the present work studies theoretically the response of the nucleosome to such external forces and how it is affected by the mechanical properties of the DNA and the presence of DNA-binding ligands.

Compressing a rigid filament: buckling and cyclization

We study elastic properties of rigid filaments modeled as stiff chains shorter than their persistence length. By rigid filaments we mean that fluctuations around the optimal filament shape are weak and that low-order expansions (quadratic or quartic) in the deviation from the optimal shape are sufficient to describe them. Our main interest lies in the profiles of force vs. projected filament length, closure probability and weakly buckled states. Results may be relevant to experiments on self-assembled biological (microtubules, actin filaments) and synthetic (organo-gelators) filaments, carbon nanotubes and polymers grafted with strongly repelling side chains, some of which are discussed here.

Formation and positioning of nucleosomes: effect of sequence-dependent long-range correlated structural disorder

The understanding of the long-range correlations (LRC) observed in DNA sequences is still an open and very challenging problem. In this paper, we start reviewing recent results obtained when exploring the scaling properties of eucaryotic, eubacterial and archaeal genomic sequences using the space-scale decomposition provided by the wavelet transform (WT). These results suggest that the existence of LRC up to distances approximately 20-30 kbp is the signature of the nucleosomal structure and dynamics of the chromatin fiber. Actually the LRC are mainly observed in the DNA bending profiles obtained when using some structural coding of the DNA sequences that accounts for the fluctuations of the local double-helix curvature within the nucleosome complex. Because of the approximate planarity of nucleosomal DNA loops, we then study the influence of the LRC structural disorder on the thermodynamical properties of 2D elastic chains submitted locally to mechanical/topological constraint as loops. The equilibrium properties of the one-loop system are derived numerically and analytically in the quite realistic weak-disorder limit. The LRC are shown to favor the spontaneous formation of small loops, the larger the LRC, the smaller the size of the loop. We further investigate the dynamical behavior of such a loop using the mean first passage time (MFPT) formalism. We show that the typical short-time loop dynamics is superdiffusive in the presence of LRC. For displacements larger than the loop size, we use large-deviation theory to derive a LRC-dependent anomalous-diffusion rule that accounts for the lack of disorder self-averaging. Potential biological implications on DNA loops involved in nucleosome positioning and dynamics in eucaryotic chromatin are discussed.

Opening of a weak link in a semiflexible ring polymer

The dynamics of contact formation between different parts of a long chain molecule is of considerable interest in biology. The related processes of opening of a loop or closing to form a loop also are of considerable interest and have attracted the attention of experimentalists/theorists. For closing, results are available in the completely flexible limit. However, this limit is not realized in many cases. Recently, there have been investigations for the semiflexible case too. We develop an approach, which leads to an easy description of the dynamics, incorporating semiflexibility rigorously into account. With this approach, the dynamics of a semiflexible polymer ring formed by a weak bond between the two ends can be modeled as the escape of a particle over a barrier in a multidimensional potential energy surface. We then calculate the rate of opening using a multidimensional transition state theory. Effects of friction on the rate are also taken into account using the standard coupling to a bath of harmonic oscillators. We find that for shorter chains (i.e., semiflexible), the rate of opening is strongly length dependent and is well described by the equation A(L/lp)v exp(Blp/L), with L as the length, and lp as the persistence length, A, B as the constants, and v approximately 1.2.

The nucleosome: a transparent, slippery, sticky and yet stable DNA-protein complex

Roughly three quarters of eucaryotic DNA are tightly wrapped onto protein cylinders organized in so-called nucleosomes. Despite this fact, the wrapped DNA cannot be inert since DNA is at the heart of many crucial life processes. We focus here on physical mechanisms that might allow nucleosomes to perform a great deal of such processes, specifically 1) on unwrapping fluctuations that give DNA-binding proteins access to the wrapped DNA portions without disrupting the nucleosome as a whole, 2) on corkscrew sliding along DNA and some implications and on 3) tail-bridging-induced attraction between nucleosomes as a means of controlling higher-order folding.

Statics and Dynamics of Polymer-Wrapped Colloids

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.

Thermodynamics of DNA loops with long-range correlated structural disorder

We study the influence of a structural disorder on the thermodynamical properties of 2D-elastic chains submitted to mechanical/topological constraint as loops. The disorder is introduced via a spontaneous curvature whose distribution along the chain presents either no correlation or long-range correlations (LRC). The equilibrium properties of the one-loop system are derived numerically and analytically for weak disorder. LRC are shown to favor the formation of small loop, larger the LRC, smaller the loop size. We use the mean first passage time formalism to show that the typical short time loop dynamics is superdiffusive in the presence of LRC. Potential biological implications on nucleosome positioning and dynamics in eukaryotic chromatin are discussed.

Formation of loops in DNA under tension

We study the formation of loops along a DNA molecule under applied tension, as might occur in single-DNA micromanipulation experiments with proteins which are able to simultaneously bind two DNA sites. We consider the case of "bare" DNA in the loop, which forms a "teardrop" shape, and the case where a single DNA-bending protein produces a "kink" in the middle of the loop; the presence of a right-angle kink in the loop reduces its bending energy by a factor of 3. Using the bending energy plus an estimate of the free energies associated with fluctuations and the elasticity of the extended nonlooped DNA, we obtain a probability distribution for loops as a function of loop size and force. Force strongly suppresses formation of all loops, but suppresses large loops more severely than small ones. This quenching effect of force is reduced in the presence of a kink in the loop. We also calculate the speed at which length is absorbed into loops between arbitrary positions along the DNA (i.e., for non-sequence-specific loop forming proteins). The speed of retraction of the molecule decays as a stretched exponential function of the force with characteristic force scales depending on the geometry of the loops.

DNA-loop formation on nucleosomes shown by in situ scanning force microscopy of supercoiled DNA

The flexibility of the chromatin structure, necessary for the processing of the genomic DNA, is controlled by a number of factors where flexibility and mobility of the nucleosomes is essential. Here, the influence of DNA supercoiling on the structure of single nucleosomes is investigated. Circular supercoiled plasmid DNA sub-saturated with histones was visualized by scanning force microscopy (SFM) in aqueous solution. SFM-imaging compared with topological analysis indicates instability of nucleosomes when the salt concentration is raised from 10 mM to 100 mM NaCl. Nucleosomes were observed after the deposition to the used scanning surface, i.e. mica coated with polylysine. On the images, the nucleosomes appear with a high probability in end-loops near the apices of the superhelices. In 100 mM NaCl but not in 10 mM NaCl, a significant number of complexes present the nucleosomes on superhelical crossings mainly located adjacent to an end-loop. The morphology of these structures and statistical analysis suggest that DNA loops were formed on the histone octamers, where the loop size distribution shows a pronounced peak at 50 nm. Recently, the formation and diffusion of loops on octamers has been discussed as a mechanism of translocations of nucleosomes along DNA. The presented data likely confirm the occurrence of loops, which may be stabilized by supercoiling. Analysis of the structure of regular nucleosomes not located on crossings indicates that reducing the salt concentration leads to more conformations, where DNA is partially unwrapped from the distal ends of the octamer.

Theory of Nucleosome Corkscrew Sliding in the Presence of Synthetic DNA Ligands

Histone octamers show a heat-induced mobility along DNA. Recent theoretical studies have established two mechanisms that are qualitatively and quantitatively compatible with in vitro experiments on nucleosome sliding: octamer repositioning through one-base-pair twist defects and through ten-base-pair bulge defects. A recent experiment demonstrated that the repositioning is strongly suppressed in the presence of minor-groove binding DNA ligands. In the present study, we give a quantitative theory for nucleosome repositioning in the presence of such ligands. We show that the experimentally observed octamer mobilities are consistent with the picture of bound ligands blocking the passage of twist defects through the nucleosome. This strongly supports the model of twist defects inducing a corkscrew motion of the nucleosome as the underlying mechanism of nucleosome sliding. We provide a theoretical estimate of the nucleosomal mobility without adjustable parameters, as a function of ligand concentration, binding affinity, binding site orientation, temperature and DNA anisotropy. Having this mobility in hand, we speculate on the interaction between a nucleosome and a transcribing RNA polymerase, and suggest a novel mechanism that might account for polymerase-induced nucleosome repositioning on short DNA templates.