A new Monte Carlo model for the structure of chromatin is presented here. Based on our previous work on superhelical DNA and polynucleosomes, it reintegrates aspects of the "solenoid" and the "zig-zag" models. The DNA is modeled as a flexible elastic polymer chain, consisting of segments connected by elastic bending, torsional, and stretching springs. The electrostatic interaction between the DNA segments is described by the Debye-Hückel approximation. Nucleosome core particles are represented by oblate ellipsoids; their interaction potential has been parameterized by a comparison with data from liquid crystals of nucleosome solutions. DNA and chromatosomes are linked either at the surface of the chromatosome or through a rigid nucleosome stem. Equilibrium ensembles of 100-nucleosome chains at physiological ionic strength were generated by a Metropolis-Monte Carlo algorithm. For a DNA linked at the nucleosome stem and a nucleosome repeat of 200 bp, the simulated fiber diameter of 32 nm and the mass density of 6.1 nucleosomes per 11 nm fiber length are in excellent agreement with experimental values from the literature. The experimental value of the inclination of DNA and nucleosomes to the fiber axis could also be reproduced. Whereas the linker DNA connects chromatosomes on opposite sides of the fiber, the overall packing of the nucleosomes leads to a helical aspect of the structure. The persistence length of the simulated fibers is 265 nm. For more random fibers where the tilt angles between two nucleosomes are chosen according to a Gaussian distribution along the fiber, the persistence length decreases to 30 nm with increasing width of the distribution, whereas the other observable parameters such as the mass density remain unchanged. Polynucleosomes with repeat lengths of 212 bp also form fibers with the expected experimental properties. Systems with larger repeat length form fibers, but the mass density is significantly lower than the measured value. The theoretical characteristics of a fiber with a repeat length of 192 bp where DNA and nucleosomes are connected at the core particle are in agreement with the experimental values. Systems without a stem and a repeat length of 217 bp do not form fibers.

Based on model structures with atomic resolution, a coarse-grained model for the nucleosome geometry was implemented. The dependence of the chromatin fiber conformation on the spatial orientation of nucleosomes and the path and length of the linker DNA was systematically explored by Monte Carlo simulations. Two fiber types were analyzed in detail that represent nucleosome chains without and with linker histones, respectively: two-start helices with crossed-linker DNA (CL conformation) and interdigitated one-start helices (ID conformation) with different nucleosome tilt angles. The CL conformation was derived from a tetranucleosome crystal structure that was extended into a fiber. At thermal equilibrium, the fiber shape persisted but relaxed into a structure with a somewhat lower linear mass density of 3.1 +/- 0.1 nucleosomes/11 nm fiber. Stable ID fibers required local nucleosome tilt angles between 40 degrees and 60 degrees. For these configurations, much higher mass densities of up to 7.9 +/- 0.2 nucleosomes/11 nm fiber were obtained. A model is proposed, in which the transition between a CL and ID fiber is mediated by relatively small changes of the local nucleosome geometry. These were found to be in very good agreement with changes induced by linker histone H1 binding as predicted from the high resolution model structures.

DNA-DNA interactions are important for the assembly of DNA nanostructures and during biological processes such as genome compaction and transcription regulation. In studies of these complex processes, DNA is commonly modeled as a homogeneously charged cylinder and its electrostatic interactions are calculated within the framework of the Poisson-Boltzmann equation. Commonly, a charge adaptation factor is used to address limitations of this theoretical approach. Despite considerable theoretical and experimental efforts, a rigorous quantitative assessment of this parameter is lacking. Here, we comprehensively characterized DNA-DNA interactions in the presence of monovalent ions by analyzing the supercoiling behavior of single DNA molecules held under constant tension. Both a theoretical model and coarse-grained simulations of this process revealed a surprisingly small effective DNA charge of 40% of the nominal charge density. These findings were directly supported by atomic-scale molecular dynamics simulations that determined the effective force between two DNA molecules. Our new parameterization has direct impact on many physical models involving DNA-DNA interactions.

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The folding of the nucleosome chain into a chromatin fiber modulates DNA accessibility and is therefore an important factor for the control of gene expression. The fiber conformation depends crucially on the interaction between individual nucleosomes. However, this parameter has not been accurately determined experimentally, and it is affected by posttranslational histone modifications and binding of chromosomal proteins. Here, the effect of different internucleosomal interaction strengths on the fiber conformation was investigated by Monte Carlo computer simulations. The fiber geometry was modeled to fit that of chicken erythrocyte chromatin, which has been examined in numerous experimental studies. In the Monte Carlo simulation, the nucleosome shape was described as an oblate spherocylinder, and a replica exchange protocol was developed to reach thermal equilibrium for a broad range of internucleosomal interaction energies. The simulations revealed the large impact of the nucleosome geometry and the nucleosome repeat length on the compaction of the chromatin fiber. At high internucleosomal interaction energies, a lateral self-association of distant fiber parts and an interdigitation of nucleosomes were apparent. These results identify key factors for the control of the compaction and higher order folding of the chromatin fiber.

The nucleosome complex of DNA wrapped around a histone protein octamer organizes the genome of eukaryotes and regulates the access of protein factors to the DNA. We performed molecular dynamics simulations of the nucleosome in explicit water to study the dynamics of its histone-DNA interactions. A high-resolution histone-DNA interaction map was derived that revealed a five-nucleotide periodicity, in which the two DNA strands of the double helix made alternating contacts. On the 100-ns timescale, the histone tails mostly maintained their initial positions relative to the DNA, and the spontaneous unwrapping of DNA was limited to 1-2 basepairs. In steered molecular dynamics simulations, external forces were applied to the linker DNA to investigate the unwrapping pathway of the nucleosomal DNA. In comparison with a nucleosome without the unstructured N-terminal histone tails, the following findings were obtained: 1), Two main barriers during unwrapping were identified at DNA position ±70 and ±45 basepairs relative to the central DNA basepair at the dyad axis. 2), DNA interactions of the histone H3 N-terminus and the histone H2A C-terminus opposed the initiation of unwrapping. 3), The N-terminal tails of H2A, H2B, and H4 counteracted the unwrapping process at later stages and were essential determinants of nucleosome dynamics. Our detailed analysis of DNA-histone interactions revealed molecular mechanisms for modulating access to nucleosomal DNA via conformational rearrangements of its structure.

The three-dimensional structure of chromatin affects DNA accessibility and is therefore a key regulator of gene expression. However, the path of the DNA between consecutive nucleosomes, and the resulting chromatin fiber organization remain controversial. The conformational space available for the folding of the nucleosome chain has been analytically described by phase diagrams with a two-angle model, which describes the chain trajectory by a DNA entry-exit angle at the nucleosome and a torsion angle between consecutive nucleosomes. Here, a novel type of numerical phase diagrams is introduced that relates the geometric phase space to the energy associated with a given chromatin conformation. The resulting phase diagrams revealed differences in the energy landscape that reflect the probability of a given conformation to form in thermal equilibrium. Furthermore, we investigated the effects of entropy and additional degrees of freedom in the dynamic phase diagrams by performing Monte Carlo simulations of the initial chain trajectories. Using our approach, we were able to demonstrate that conformations that initially were geometrically impossible could evolve into energetically favorable states in thermal equilibrium due to DNA bending and torsion. In addition, dynamic phase diagrams were applied to identify chromatin fibers that reflect certain experimentally determined features.

BackgroundThe rearrangement of nucleosomes along the DNA fiber profoundly affects gene expression, but little is known about how signalling reshapes the chromatin landscape, in three-dimensional space and over time, to allow establishment of new transcriptional programs.ResultsUsing micrococcal nuclease treatment and high-throughput sequencing, we map genome-wide changes in nucleosome positioning in primary human endothelial cells stimulated with tumour necrosis factor alpha (TNFα) - a proinflammatory cytokine that signals through nuclear factor kappa-B (NF-κB). Within 10 min, nucleosomes reposition at regions both proximal and distal to NF-κB binding sites, before the transcription factor quantitatively binds thereon. Similarly, in long TNFα-responsive genes, repositioning precedes transcription by pioneering elongating polymerases and appears to nucleate from intragenic enhancer clusters resembling super-enhancers. By 30 min, widespread repositioning throughout megabase pair-long chromosomal segments, with consequential effects on three-dimensional structure (detected using chromosome conformation capture), is seen.ConclusionsWhilst nucleosome repositioning is viewed as a local phenomenon, our results point to effects occurring over multiple scales. Here, we present data in support of a TNFα-induced priming mechanism, mostly independent of NF-κB binding and/or elongating RNA polymerases, leading to a plastic network of interactions that affects DNA accessibility over large domains.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-014-0536-6) contains supplementary material, which is available to authorized users.