A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

Geometrical correlations in the nucleosomal DNA conformation and the role of the covalent bonds rigidity

We develop a simple elastic model to study the conformation of DNA in the nucleosome core particle. In this model, the changes in the energy of the covalent bonds that connect the base pairs of each strand of the DNA double helix, as well as the lateral displacements and the rotation of adjacent base pairs are considered. We show that because of the rigidity of the covalent bonds in the sugar-phosphate backbones, the base pair parameters are highly correlated, especially, strong twist-roll-slide correlation in the conformation of the nucleosomal DNA is vividly observed in the calculated results. This simple model succeeds to account for the detailed features of the structure of the nucleosomal DNA, particularly, its more important base pair parameters, roll and slide, in good agreement with the experimental results.     

Molecular Dynamics Simulations of a Nucleosome and Free DNA

Abstract

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Structure-based Analysis of DNA Sequence Patterns Guiding Nucleosome Positioning in vitro

Abstract

Recent studies of genome-wide nucleosomal organization suggest that the DNA sequence is one of the major determinants of nucleosome positioning. Although the search for underlying patterns encoded in nucleosomal DNA has been going on for about 30 years, our knowledge of these patterns still remains limited. Based on our evaluations of DNA deformation energy, we developed new scoring functions to predict nucleosome positioning. There are three principal differences between our approach and earlier studies: (i) we assume that the length of nucleosomal DNA varies from 146 to 147 bp; (ii) we consider the anisotropic flexibility of pyrimidine-purine (YR) dimeric steps in the context of their neighbors (e.g., YYRR versus RYRY); (iii) we postulate that alternating AT-rich and GC-rich motifs reflect sequence-dependent interactions between histone arginines and DNA in the minor groove. Using these functions, we analyzed 20 nucleosome positions mapped in vitro at single nucleotide resolution (including clones 601, 603, 605, the pGUB plasmid, chicken β-globin and three 5S rDNA genes). We predicted 15 of the 20 positions with 1-bp precision, and two positions with 2-bp precision. The predicted position of the ‘601’ nucleosome (i.e., the optimum of the computed score) deviates from the experimentally determined unique position by no more than 1 bp—an accuracy exceeding that of earlier predictions.

Our analysis reveals a clear heterogeneity of the nucleosomal sequences which can be divided into two groups based on the positioning ‘rules’ they follow. The sequences of one group are enriched by highly deformable YR/YYRR motifs at the minor-groove bending sites SHL ±3.5 and ±5.5, which is similar to the α-satellite sequence used in most crystallized nucleosomes. Apparently, the positioning of these nucleosomes is determined by the interactions between histones H2A/H2B and the terminal parts of nucleosomal DNA. In the other group (that includes the ‘601’ clone) the same YR/YYRR motifs occur predominantly at the sites SHL ±1.5. The interaction between the H3/H4 tetramer and the central part of the nucleosomal DNA is likely to be responsible for the positioning of nucleosomes of this group, and the DNA trajectory in these nucleosomes may differ in detail from the published structures.

Thus, from the stereochemical perspective, the in vitro nucleosomes studied here follow either an X-ray-like pattern (with strong deformations in the terminal parts of nucleosomal DNA), or an alternative pattern (with the deformations occurring predominantly in the central part of the nucleosomal DNA). The results presented here may be useful for genome-wide classification of nucleosomes, linking together structural and thermodynamic characteristics of nucleosomes with the underlying DNA sequence patterns guiding their positions.     

Using DNA mechanics to predict in vitro nucleosome positions and formation energies

In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone–DNA interactions.     

DNA conformation and energy in nucleosome core: a theoretical approach

DNA conformation in complex with proteins is far from its canonical B-form. The affinity of complex formation and structure of DNA depend on its attachment configuration and sequence. In this article, we develop a mechanical model to address the problem of DNA structure and energy under deformation. DNA in nucleosome core particle is described as an example. The structure and energy of nucleosomal DNA is calculated based on its sequence and positioning state. The inferred structure has remarkable similarity with X-ray data. Although there is no sequence-specific interaction of bases and the histone core, we found considerable sequence dependency for the nucleosomal DNA positioning. The affinity of nucleosome formation for several sequences is examined and the differences are compatible with observations. We argue that structural energy determines the natural state of nucleosomal DNA and is the main reason for affinity differences in vitro. This theory can be utilized for the DNA structure and energy determination in protein–DNA complexes in general.

An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:17     

Molecular dynamics simulations of a nucleosome and free DNA

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Calculation of radiation-induced DNA damage from photons and tritium beta-particles

Radiation-induced damage in nucleosomal DNA was modelled by Monte Carlo means. An atomistic representation of DNA with a first hydration shell was used. DNA single- and double-strand break (SSB and DSB) yields were calculated for ¹³⁷Cs photons, x-rays and tritium beta-particles. Monte Carlo-generated electron tracks for liquid water were used to model energy deposition. Chemical evolution of a track and interactions between species and DNA following water radiolysis were modelled in an encounter-controlled manner. The effects of varying the scavenging capacity of the environment, the extent of DNA protection by histones and the setting of a threshold for direct energy depositions on DNA break yields were all systematically studied. DSB complexity was assessed in terms of DNA breaks and base damage accompanying a DSB. Model parameters were adjusted to make predictions consistent with experimental data on DSB yields and yield modification by a variety of factors including changing DNA conformation and incorporation of scavengers. An embedded model of nucleosomal DNA by histones was required to explain experimentally observed modification of DSB yield by removal of bound histones. Complex DSB, defined as DSB accompanied by an additional strand breakage, exhibited high association with base damage. It is shown that hydroxyl radical interactions with bases are a major contributor to DSB complexity. On average there were 1.15 and 2.69 OH-base interactions accompanying simple and complex DSB, respectively for ¹³⁷Cs. Over 80% of complex DSB had at least one OH-base interaction associated with a DNA break. Received: 21 March 2000 / Accepted: 27 October 2000     

Dynamics of nucleosome invasion by DNA binding proteins

Nucleosomes sterically occlude their wrapped DNA from interacting with many large protein complexes. How proteins gain access to nucleosomal DNA target sites in vivo is not known. Outer stretches of nucleosomal DNA spontaneously unwrap and rewrap with high frequency, providing rapid and efficient access to regulatory DNA target sites located there; however, rates for access to the nucleosome interior have not been measured. Here we show that for a selected high-affinity nucleosome positioning sequence, the spontaneous DNA unwrapping rate decreases dramatically with distance inside the nucleosome. The rewrapping rate also decreases, but only slightly. Our results explain the previously known strong position dependence on the equilibrium accessibility of nucleosomal DNA, which is characteristic of both selected and natural sequences. Our results point to slow nucleosome conformational fluctuations as a potential source of cell-cell variability in gene activation dynamics, and they reveal the dominant kinetic path by which multiple DNA binding proteins cooperatively invade a nucleosome.     

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed “cold sites”, which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.     

Theoretical study of structural transition in a nucleosome at low ionic strength

The theoretical analysis of nucleosome stability at low ionic strength has been performed on the basis of consideration of different contributions to the free energy of compact state of the nucleosome DNA terminal regions. The proposed model explains: the fact of low-salt structural change; the transition point (approximately 1.7 mM NaCl) and width (approximately 1 mM); the shift of the transition to the higher salt concentrations in the case of histones tails removal by trypsin. According to the model the increase of electrostatic repulsion between neighbouring turns of DNA superhelix is the main cause of the unwinding of nucleosomal DNA terminal regions in the course of low-salt structural change. The interactions between histone (H2A-H2B) dimer and (H3-H4)2 tetramer provide the compact state of the nucleosomal DNA terminal regions. The existence of electrostatic interactions of nucleosomal DNA terminal regions with tetramer was suggested. These interactions can provide the compact state of nucleosomal DNA at physiological ionic strength even in the absence of (H2A-H2B) dimer.     

A computational study of nucleosomal DNA flexibility

Molecular dynamics simulations of the nucleosome core particle and its isolated DNA free in solution are reported. The simulations are based on the implicit solvent methodology and provide insights into the nature of large-scale structural fluctuations and flexibility of the nucleosomal DNA. In addition to the kinked regions previously identified in the x-ray structure of the nucleosome, the simulations support the existence of a biochemically identified distorted region of the DNA. Comparison of computed relative free energies shows that formation of the kinks is associated with little, if any, energy cost relative to a smooth, ideal conformation of the DNA superhelix. Isolated nucleosomal DNA is found to be considerably more flexible than expected for a 147 bp stretch of DNA based on its canonical persistence length of 500 A. Notably, the significant bending of the DNA observed in our simulations occurs without breaking of Watson-Crick bonds. The computed relative stability of bent conformations is sensitive to the ionic strength of the solution in the physiological range; the sensitivity suggests possible experiments that might provide further insights into the structural origins of the unusual flexibility of the DNA.     

Dual role of DNA intrinsic curvature and flexibility in determining nucleosome stability

A statistical mechanistic approach to evaluate the sequence-dependent thermodynamic stability of nucleosomes is proposed. The model is based on the calculation of the DNA intrinsic curvature, obtained by integrating the nucleotide step deviations from the canonical B-DNA structure, and on the evaluation of the first order elastic distortion energy to reach the nucleosomal superstructure. Literature data on the free energy of nucleosome formation as obtained by competitive nucleosome reconstitution of a significant pool of different DNA sequences were compared with the theoretical results, and a satisfactorily good correlation was found. A striking result of the comparison is the emergence of two opposite roles of the DNA intrinsic curvature and flexibility in determining nucleosome stability. Finally, the obtained results suggest that the curvature-dependent DNA hydration should play a relevant role in the sequence-dependent nucleosome stability.     

The Molecular Evolution of Nucleosome Positioning Through Sequence-Dependent Deformation of the DNA Polymer

Abstract

The computational prediction of nucleosome positioning from DNA sequence now allows for in silico investigation of the molecular evolution of biophysical properties of the DNA molecule responsible for primary chromatin organization in the genome. To discern what signal components driving nucleosome positioning in the yeast genome are potentially targeted by natural selection, we compare the performance of various models predictive of nucleosome positioning within the context of a simple statistical test, the repositioned mutation test. We demonstrate that while nucleosome occupancy is driven largely by translational exclusion in response to AT content, there is also a strong signature of evolutionary conservation of regular patterns within nucleosomal DNA sequence related to the structural organization of the nucleosome core (e.g., 10-bp dinucleotide periodicity). We also use computer simulations to investigate hypothetical coding and regulatory constraints on the ability of sequence properties affecting nucleosome formation to adaptively evolve. Our results demonstrate that natural selection may act independently on different DNA sequence properties responsible for local chromatin organization. Furthermore, at least with respect to the deformation energy of the DNA molecule in the nucleosome, the presence of the genetic code has greatly restricted the ability of sequences to evolve the dynamic nucleosome organization typically observed in promoter regions.     

Effects of DNA looping on pyrimidine dimer formation.

We have assessed the effects of DNA curvature on pyrimidine dimer (PD) formation by examining the pattern of PD formation in DNA held in a loop by lambda repressor. The loop region was composed of diverse DNA sequences such that potential PD sites occurred throughout the loop. PD formation in the loop occurred with peaks at approximately 10 base intervals, just 3' of where the bending of the DNA was inferred to be toward the major groove. This relationship between the peaks and the DNA curvature is essentially identical to that observed in the nucleosome. This indicates that DNA curvature is the major source of the periodicity of PD formation in the nucleosome, and supports an earlier model of the conformation of nucleosomal DNA based on PD formation. DNA loops containing diverse sequences should be of general value for assessing the effects of DNA curvature on DNA modification by other agents used to probe DNA-protein interactions and DNA conformation.     

A statistical thermodynamic model applied to experimental AFM population and location data is able to quantify DNA-histone binding strength and internucleosomal interaction differences between acetylated and unacetylated nucleosomal arrays

Imaging of nucleosomal arrays by atomic force microscopy allows a determination of the exact statistical distributions for the numbers of nucleosomes per array and the locations of nucleosomes on the arrays. This precision makes such data an excellent reference for testing models of nucleosome occupation on multisite DNA templates. The approach presented here uses a simple statistical thermodynamic model to calculate theoretical population and positional distributions and compares them to experimental distributions previously determined for 5S rDNA nucleosomal arrays (208-12,172-12). The model considers the possible locations of nucleosomes on the template, and takes as principal parameters an average free energy of interaction between histone octamers and DNA, and an average wrapping length of DNA around the octamers. Analysis of positional statistics shows that it is possible to consider interactions between nucleosomes and positioning effects as perturbations on a random positioning noninteracting model. Analysis of the population statistics is used to determine histone-DNA association constants and to test for differences in the free energies of nucleosome formation with different types of histone octamers, namely acetylated or unacetylated, and different DNA templates, namely 172-12 or 208-12 5S rDNA multisite templates. The results show that the two template DNAs bind histones with similar affinities but histone acetylation weakens the association of histones with both templates. Analysis of locational statistics is used to determine the strength of specific nucleosome positioning tendencies by the DNA templates, and the strength of the interactions between neighboring nucleosomes. The results show only weak positioning tendencies and that unacetylated nucleosomes interact much more strongly with one another than acetylated nucleosomes; in fact acetylation appears to induce a small anticooperative occupation effect between neighboring nucleosomes.