Nucleosome geometry and internucleosomal interactions control the chromatin fiber conformation

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° and 60°. 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.     

Nucleosome gaping supports a functional structure for the 30nm chromatin fiber

The biological functions played by the nucleus of eukaryotic cells and especially those involved in cellular differentiation not only depend on the genomic sequence but also on all the proteins which form the nucleo-protein complex named chromatin. The tridimensional organization of this huge polymer involves many structural levels, the most basic one being the nucleosome. Nucleosomes further organize into the so-called 30nm fiber, which, according to recent works, is likely to be the main functional level of chromatin. We wish here to propose a plausible structure for the 30nm chromatin fiber that could explain its functional role. In our model, silenced chromatin is locked by nucleosome stacking interactions. This is achieved by a conformational transition within the nucleosome core particle (NCP) which allows nucleosomes to stack along two helices without bending the DNA linkers. We used molecular modeling to check that this conformational transition was plausible. Then we proposed to modify the well-known two-angle model according to these atomic level results. The emerging picture is an allosteric behavior of the nucleosomes induced by their collective organization within the 30nm chromatin fiber.     

An all-atom model of the chromatin fiber containing linker histones reveals a versatile structure tuned by the nucleosomal repeat length

In the nucleus of eukaryotic cells, histone proteins organize the linear genome into a functional and hierarchical architecture. In this paper, we use the crystal structures of the nucleosome core particle, B-DNA and the globular domain of H5 linker histone to build the first all-atom model of compact chromatin fibers. In this 3D jigsaw puzzle, DNA bending is achieved by solving an inverse kinematics problem. Our model is based on recent electron microscopy measurements of reconstituted fiber dimensions. Strikingly, we find that the chromatin fiber containing linker histones is a polymorphic structure. We show that different fiber conformations are obtained by tuning the linker histone orientation at the nucleosomes entry/exit according to the nucleosomal repeat length. We propose that the observed in vivo quantization of nucleosomal repeat length could reflect nature's ability to use the DNA molecule's helical geometry in order to give chromatin versatile topological and mechanical properties.     

On the role of inter-nucleosomal interactions and intrinsic nucleosome dynamics in chromatin function

Evidence is emerging that many diseases result from defects in gene functions, which, in turn, depend on the local chromatin environment of a gene. However, it still remains not fully clear how chromatin activity code is ‘translated’ to the particular ‘activating’ or ‘repressing’ chromatin structural transition. Commonly, chromatin remodeling in vitro was studied using mononucleosomes as a model. However, recent data suggest that structural reorganization of a single mononucleosome is not equal to remodeling of a nucleosome particle under multinucleosomal content – such as, interaction of nucleosomes via flexible histone termini could significantly alter the mode (and the resulting products) of nucleosome structural transitions. It is becoming evident that a nucleosome array does not constitute just a ‘polymer’ of individual ‘canonical’ nucleosomes due to multiple inter-nucleosomal interactions which affect nucleosome dynamics and structure. It could be hypothesized, that inter-nucleosomal interactions could act in cooperation with nucleosome inherent dynamics to orchestrate DNA-based processes and promote formation and stabilization of highly-dynamic, accessible structure of a nucleosome array. In the proposed paper we would like to discuss the nucleosome dynamics within the chromatin fiber mainly as it pertains to the roles of the structural changes mediated by inter-nucleosomal interactions.     

Changing Chromatin Fiber Conformation by Nucleosome Repositioning

Chromatin conformation is dynamic and heterogeneous with respect to nucleosome positions, which can be changed by chromatin remodeling complexes in the cell. These molecular machines hydrolyze ATP to translocate or evict nucleosomes, and establish loci with regularly and more irregularly spaced nucleosomes as well as nucleosome-depleted regions. The impact of nucleosome repositioning on the three-dimensional chromatin structure is only poorly understood. Here, we address this issue by using a coarse-grained computer model of arrays of 101 nucleosomes considering several chromatin fiber models with and without linker histones, respectively. We investigated the folding of the chain in dependence of the position of the central nucleosome by changing the length of the adjacent linker DNA in basepair steps. We found in our simulations that these translocations had a strong effect on the shape and properties of chromatin fibers: i), Fiber curvature and flexibility at the center were largely increased and long-range contacts between distant nucleosomes on the chain were promoted. ii), The highest destabilization of the fiber conformation occurred for a nucleosome shifted by two basepairs from regular spacing, whereas effects of linker DNA changes of ∼10 bp in phase with the helical twist of DNA were minimal. iii), A fiber conformation can stabilize a regular spacing of nucleosomes inasmuch as favorable stacking interactions between nucleosomes are facilitated. This can oppose nucleosome translocations and increase the energetic costs for chromatin remodeling. Our computational modeling framework makes it possible to describe the conformational heterogeneity of chromatin in terms of nucleosome positions, and thus advances theoretical models toward a better understanding of how genome compaction and access are regulated within the cell.     

Computer simulation of the 30-nanometer chromatin fiber

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.     

Involvement of histone H1 in the organization of the nucleosome and of the salt-dependent superstructures of chromatin

We describe the results of a systematic study, using electron microscopy, of the effects of ionic strength on the morphology of chromatin and of H1-depleted chromatin. With increasing ionic strength, chromatin folds up progressively from a filament of nucleosomes at approximately 1 mM monovalent salt through some intermediate higher- order helical structures (Thoma, F., and T. Koller, 1977, Cell 12:101- 107) with a fairly constant pitch but increasing numbers of nucleosomes per turn, until finally at 60 mM (or else in approximately 0.3 mM Mg++) a thick fiber of 250 A diameter is formed, corresponding to a structurally well-organized but not perfectly regular superhelix or solenoid of pitch approximately 110 A as described by Finch and Klug (1976, Proc. Natl. Acad. Sci. U.S.A. 73:1897-1901). The numbers of nucleosomes per turn of the helical structures agree well with those which can be calculated from the light-scattering data of Campbell et al. (1978, Nucleic Acids Res. 5:1571-1580). H1-depleted chromatin also condenses with increasing ionic strength but not so densely as chromatin and not into a definite structure with a well-defined fiber direction. At very low ionic strengths, nucleosomes are present in chromatin but not in H1-depleted chromatin which has the form of an unravelled filament. At somewhat higher ionic strengths (greater than 5 mM triethanolamine chloride), nucleosomes are visible in both types of specimen but the fine details are different. In chromatin containing H1, the DNA enters and leaves the nucleosome on the same side but in chromatin depleted of H1 the entrance and exit points are much more random and more or less on opposite sides of the nucleosome. We conclude that H1 stabilizes the nucleosome and is located in the region of the exit and entry points of the DNA. This result is correlated with biochemical and x-ray crystallographic results on the internal structure of the nucleosome core to give a picture of a nucleosome in which H1 is bound to the unique region on a complete two-turn, 166 base pair particle (Fig. 15). In the formation of higher-order structures, these regions on neighboring nucleosomes come closer together so that an H1 polymer may be formed in the center of the superhelical structures.     

The effect of internucleosomal interaction on folding of the chromatin fiber

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.     

Changing Chromatin Fiber Conformation by Nucleosome Repositioning

Chromatin conformation is dynamic and heterogeneous with respect to nucleosome positions, which can be changed by chromatin remodeling complexes in the cell. These molecular machines hydrolyze ATP to translocate or evict nucleosomes, and establish loci with regularly and more irregularly spaced nucleosomes as well as nucleosome-depleted regions. The impact of nucleosome repositioning on the three-dimensional chromatin structure is only poorly understood. Here, we address this issue by using a coarse-grained computer model of arrays of 101 nucleosomes considering several chromatin fiber models with and without linker histones, respectively. We investigated the folding of the chain in dependence of the position of the central nucleosome by changing the length of the adjacent linker DNA in basepair steps. We found in our simulations that these translocations had a strong effect on the shape and properties of chromatin fibers: i), Fiber curvature and flexibility at the center were largely increased and long-range contacts between distant nucleosomes on the chain were promoted. ii), The highest destabilization of the fiber conformation occurred for a nucleosome shifted by two basepairs from regular spacing, whereas effects of linker DNA changes of ∼10 bp in phase with the helical twist of DNA were minimal. iii), A fiber conformation can stabilize a regular spacing of nucleosomes inasmuch as favorable stacking interactions between nucleosomes are facilitated. This can oppose nucleosome translocations and increase the energetic costs for chromatin remodeling. Our computational modeling framework makes it possible to describe the conformational heterogeneity of chromatin in terms of nucleosome positions, and thus advances theoretical models toward a better understanding of how genome compaction and access are regulated within the cell.     

Quantitative analysis of single-molecule force spectroscopy on folded chromatin fibers

Single-molecule techniques allow for picoNewton manipulation and nanometer accuracy measurements of single chromatin fibers. However, the complexity of the data, the heterogeneity of the composition of individual fibers and the relatively large fluctuations in extension of the fibers complicate a structural interpretation of such force-extension curves. Here we introduce a statistical mechanics model that quantitatively describes the extension of individual fibers in response to force on a per nucleosome basis. Four nucleosome conformations can be distinguished when pulling a chromatin fiber apart. A novel, transient conformation is introduced that coexists with single wrapped nucleosomes between 3 and 7 pN. Comparison of force-extension curves between single nucleosomes and chromatin fibers shows that embedding nucleosomes in a fiber stabilizes the nucleosome by 10 k_BT. Chromatin fibers with 20- and 50-bp linker DNA follow a different unfolding pathway. These results have implications for accessibility of DNA in fully folded and partially unwrapped chromatin fibers and are vital for understanding force unfolding experiments on nucleosome arrays.     

Exploring the Conformational Space of Chromatin Fibers and Their Stability by Numerical Dynamic Phase Diagrams

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.     

Methods for chromatin assembly and remodeling

Packaging of the DNA in nucleosomes restricts its accessibility to regulatory factors and enzymatic complexes, making a local remodeling of the nucleosome structure a prerequisite to the establishment of protein-DNA interactions. The use of an experimental system in which one nucleosome is reconstituted on a short linear DNA fragment allows gel fractionation of nucleosomes according to their translational positions, whose locations are dependent on the underlying DNA sequence. Nucleosome mobilization by chromatin remodeling factors is easily detected by observing band disappearance in gel, which in turn provides evidence for histone octamer displacement. Here, we provide methods for chromatin assembly that we have been using in our analysis for nucleosome mobilization by chromatin remodeling factors. These methods are straightforward and easy to follow. Thus, they may provide a good starting assay system for analysis of nucleosome movements by other chromatin remodeling machines.     

Nucleosome positioning in relation to nucleosome spacing and DNA sequence-specific binding of a protein

Nucleosome positioning is an important mechanism for the regulation of eukaryotic gene expression. Folding of the chromatin fiber can influence nucleosome positioning, whereas similar electrostatic mechanisms govern the nucleosome repeat length and chromatin fiber folding in vitro. The position of the nucleosomes is directed either by the DNA sequence or by the boundaries created due to the binding of certain trans-acting factors to their target sites in the DNA. Increasing ionic strength results in an increase in nucleosome spacing on the chromatin assembled by the S-190 extract of Drosophila embryos. In this study, a mutant lac repressor protein R3 was used to find the mechanisms of nucleosome positioning on a plasmid with three R3-binding sites. With increasing ionic strength in the presence of R3, the number of positioned nucleosomes in the chromatin decreased, whereas the internucleosomal spacings of the positioned nucleosomes in a single register did not change. The number of the positioned nucleosomes in the chromatin assembled in vitro over different plasmid DNAs with 1-3 lac operators changed with the relative position and number of the R3-binding sites. We found that in the presence of R3, nucleosomes were positioned in the salt gradient method of the chromatin assembly, even in the absence of a nucleosome-positioning sequence. Our results show that nucleosome-positioning mechanisms are dominant, as the nucleosomes can be positioned even in the absence of regular spacing mechanisms. The protein-generated boundaries are more effective when more than one binding site is present with a minimum distance of approximately 165 bp, greater than the nucleosome core DNA length, between them.     

A novel roll-and-slide mechanism of DNA folding in chromatin: implications for nucleosome positioning

How eukaryotic genomes encode the folding of DNA into nucleosomes and how this intrinsic organization of chromatin guides biological function are questions of wide interest. The physical basis of nucleosome positioning lies in the sequence-dependent propensity of DNA to adopt the tightly bent configuration imposed by the binding of the histone proteins. Traditionally, only DNA bending and twisting deformations are considered, while the effects of the lateral displacements of adjacent base pairs are neglected. We demonstrate, however, that these displacements have a much more important structural role than ever imagined. Specifically, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. Furthermore, the computed cost of deforming DNA on the nucleosome is sequence-specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends into the minor groove). These conclusions rest upon a treatment of DNA that goes beyond the conventional ribbon model, incorporating all essential degrees of freedom of "real" duplexes in the estimation of DNA deformation energies. Indeed, only after lateral Slide displacements are considered are we able to account for the sequence-specific folding of DNA found in nucleosome structures. The close correspondence between the predicted and observed nucleosome locations demonstrates the potential advantage of our "structural" approach in the computer mapping of nucleosome positioning.     

Small angle x-ray scattering of chromatin. Radius and mass per unit length depend on linker length.

Analyses of low angle x-ray scattering from chromatin, isolated by identical procedures but from different species, indicate that fiber diameter and number of nucleosomes per unit length increase with the amount of nucleosome linker DNA. Experiments were conducted at physiological ionic strength to obtain parameters reflecting the structure most likely present in living cells. Guinier analyses were performed on scattering from solutions of soluble chromatin from Necturus maculosus erythrocytes (linker length 48 bp), chicken erythrocytes (linker length 64 bp), and Thyone briareus sperm (linker length 87 bp). The results were extrapolated to infinite dilution to eliminate interparticle contributions to the scattering. Cross-sectional radii of gyration were found to be 10.9 +/- 0.5, 12.1 +/- 0.4, and 15.9 +/- 0.5 nm for Necturus, chicken, and Thyone chromatin, respectively, which are consistent with fiber diameters of 30.8, 34.2, and 45.0 nm. Mass per unit lengths were found to be 6.9 +/- 0.5, 8.3 +/- 0.6, and 11.8 +/- 1.4 nucleosomes per 10 nm for Necturus, chicken, and Thyone chromatin, respectively. The geometrical consequences of the experimental mass per unit lengths and radii of gyration are consistent with a conserved interaction among nucleosomes. Cross-linking agents were found to have little effect on fiber external geometry, but significant effect on internal structure. The absolute values of fiber diameter and mass per unit length, and their dependencies upon linker length agree with the predictions of the double-helical crossed-linker model. A compilation of all published x-ray scattering data from the last decade indicates that the relationship between chromatin structure and linker length is consistent with data obtained by other investigators.