Dynamics of Nucleosome Assembly and Effects of DNA Methylation

The nucleosome is the fundamental packing unit of the eukaryotic genome, and CpG methylation is an epigenetic modification associated with gene repression and silencing. We investigated nucleosome assembly mediated by histone chaperone Nap1 and the effects of CpG methylation based on three-color single molecule FRET measurements, which enabled direct monitoring of histone binding in the context of DNA wrapping. According to our observation, (H3-H4)₂ tetramer incorporation must precede H2A-H2B dimer binding, which is independent of DNA termini wrapping. Upon CpG methylation, (H3-H4)₂ tetramer incorporation and DNA termini wrapping are facilitated, whereas proper incorporation of H2A-H2B dimers is inhibited. We suggest that these changes are due to rigidified DNA and increased random binding of histones to DNA. According to the results, CpG methylation expedites nucleosome assembly in the presence of abundant DNA and histones, which may help facilitate gene packaging in chromatin. The results also indicate that the slowest steps in nucleosome assembly are DNA termini wrapping and tetramer positioning, both of which are affected heavily by changes in the physical properties of DNA.     

Nucleosome DNA Bendability Matrix (C. elegans)

Abstract

An original signal extraction procedure is applied to database of 146 base nucleosome core DNA sequences from C. elegans (S. M. Johnson et al. Genome Research 16, 1505–1516, 2006). The positional preferences of various dinucleotides within the 10.4 base nucleosome DNA repeat are calculated, resulting in derivation of the nucleosome DNA bendability matrix of 16x10 elements. A simplified one-line presentation of the matrix (“consensus” repeat) is…A(TTTCCGGAAA)T…. All 6 chromosomes of C. elegans conform to the bendability pattern. The strongest affinity to their respective positions is displayed by dinucleotides AT and CG, separated within the repeat by 5 bases. The derived pattern makes a basis for sequence-directed mapping of nucleosome positions in the genome of C. elegans. As the first complete matrix of bendability available the pattern may serve for iterative calculations of the species-specific matrices of bendability applicable to other genomic sequences.     

Calculating Free Energies Using a Scaled-Force Molecular Dynamics Algorithm

We propose and test a family of methods to calculate the free energy along a generalized coordinate, , based on computing the force acting on this coordinate. First, we derive a formula that connects the free energy in unconstrained simulations with the force of constraint that can be readily calculated numerically. Then, we consider two methods, which improve the efficiency of the free energy calculation by yielding uniform or nearly uniform sampling of . Both rely on modifying the force acting on . In one method, this force is replaced by a force with zero mean and is advanced quasistatically. In the second method, the force is augmented adaptively by a biasing force. We provide formulas for calculating the free energy of the unmodified system from the forces acting in these modified, non-Hamiltonian systems. Using conformational transitions in 1,2-dichloroethane as a test case, we show that both methods perform very well.     

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.     

基于DNA变形能的核小体定位预测方法研究进展

真核细胞中,作为染色质基本结构单元的核小体参与调控基因的转录、DNA复制、重组以及RNA剪接等诸多生物学过程。阐明核小体定位机制并准确预测核小体在染色体上的位置对解读染色质结构与功能有重要生物学意义。在过去30多年时间里,研究人员发展了多种预测核小体位置的方法。最理想的方法应考虑DNA序列、组蛋白修饰和染色质重塑等影响核小体定位的诸多因素,然而现实中,捕捉主要因素的模型也往往具有很高的鲁棒性和实用价值。DNA序列偏好性是在全基因组尺度上影响核小体定位的最重要因素之一,因此基于DNA序列的核小体定位预测方法也最常见。这种方法可大致分为两类,即基于DNA序列信息的生物信息学模型和基于DNA变形能的生物物理学模型。本文重点介绍生物物理学模型近些年取得的主要进展。     

Effect of Cation Concentration on Molecular Dynamics Simulations of UDP-Glucose

Abstract

Glycosyl esters of nucleoside di or mono-phosphates, generally referred to as “sugar nucleotides”, serve as a sugar donors during the biosynthesis of oligo- and polysaccharides; they are therefore of a primary importance in carbohydrate metabolism in the living world. Molecular dynamics simulations were used to explore the conformational flexibility of one nucleotide sugar, UDP-glucose (UDP-Glc). The AMBER program package was used with some new parameters especially developed for nucleotide sugars. Several simulations on this molecule in aqueous solution, each of 2 ns duration, were carried out for increasing concentrations of monovalent K⁺ and divalent Mg²⁺ ions. For the monovalent ion, it is revealed that its presence and concentration is crucial for the conformational behavior, resulting in the stabilization of the extended conformation. The preferred location of K⁺ is in close proximity to the negatively charged phosphate oxygens, but the ion moves freely and can occupy other sites. Since the size of this cation is close that of the water molecules, the hydration scheme is not perturbed. Completely different results are obtained when the divalent Mg²⁺ cation is introduced in the simulation. A very strong interaction is established between the phosphate group and the cation; as a result the UDP-Glc molecule is locked in a rigid extended geometry. The analyses of the trajectories provide new insight on the role of the metal ion in the catalytic mechanism of glycosyltransferases.     

The Role of Molecular Dynamics Simulations for the Study of Slow Dynamics

Abstract

A two step strategy is proposed to study dynamical properties of a physical system much slower than the time scales accessible by molecular dynamics simulations. The strategy is applied to investigate the slow dynamics of supercooled liquids.     

Molecular Dynamics as a Mathematical Mapping. I. Differentiable Force Functions

Abstract

The molecular dynamics technique can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and the input macroscopic conditions, and, on the other, the calculated macroscopic properties of the bulk molecular system.

The differentiability of such a mapping in the conventional molecular dynamics calculations is affected by the discontinuities in particle positions introduced by the periodic boundary conditions and the discontinuities introduced by the minimum image convention and other methods commonly employed to approximate the calculation of interparticle potential and force.

This paper proposes an alternative molecular dynamics framework based on modified force functions which are almost everywhere continuous and differentiable, and exhibit a natural periodicity. These characteristics obviate the need for both the periodic boundary conditions and the minimum image convention, as well as for any corrections for long-range interactions. They also make it possible to apply standard methods of variational calculus for the computation of partial derivatives of the molecular dynamics mapping.

The modified framework is first introduced for the case of simple monoatomic fluids where the nature of the forces exerted between any pair of two particles is identical. A more general model describing the interactions of flexible molecules is then developed. We describe the application of this approach to mixtures of alkane molecules interacting via the NERD force field.     

DNA Architecture,Deformability, and Nucleosome Positioning

Abstract

The positioning of DNA on nucleosomes is critical to both the organization and expression of the genetic message. Here we focus on DNA conformational signals found in the growing library of known high-resolution core-particle structures and the ways in which these features may contribute to the positioning of nucleosomes on specific DNA sequences. We survey the chemical composition of the protein-DNA assemblies and extract features along the DNA superhelical pathway—the minor-groove width and the deformations of successive base pairs—determined with reasonable accuracy in the structures. We also examine the extent to which the various nucleosome core-particle structures accommodate the observed settings of the crystallized sequences and the known positioning of the high-affinity synthetic ‘601’ sequence on DNA. We ‘thread’ these sequences on the different structural templates and estimate the cost of each setting with knowledge-based potentials that reflect the conformational properties of the DNA base-pair steps in other high-resolution protein-bound complexes.     

Molecular Dynamics Simulations of The Swelling of Terephthalate Containing Anionic Clays

Abstract

We report on molecular simulations of the swelling of terephthalate containing anionic clays. We find good agreement with experimentally derived interlayer spacings, and models for the structure and dynamics of the interlayer water. We predict a swelling profile which suggests that at high water content a sharp increase in interlayer spacing will occur. The corresponding swelling curve for methanol incorporation, however, indicates a more continuous expansion.     

Molecular Dynamics Simulations with Interaction Potentials Including Polarization Development of a Noniterative Method and Application to Water

A general method is suggested for the implementation of polarization in molecular dynamics simulations of small molecules. Induced dipole moments are evaluated on selected polarizability centers and represented by separation of charges. The positive polarization charges reside on the selected atoms. The negative polarization charges are treated as additional particles. The positions of these polarization charges are determined from the electrical fields due to the permanent charges of the system. Thus the induction is treated explicitly, while the higher order contributions, the polarization due to induced dipoles, are taken into account in an average way by modification of potential parameters. The forces can be evaluated for the new charge distribution in the conventional way. As an illustration of this approach initial results are reported for the development of a polarizable water model. The higher order polarization is treated in an average way by slight increase of the permanent charges as compared to the values that would give the gas phase dipole moment. The increase in CPU time is comparable to the addition of one atom per polarizable center.     

Molecular Dynamics Simulations of Alumina Addition in Sodium Silicate Glasses

Abstract

Molecular dynamics simulations of alumina containing silicate glasses have been performed in order to determine the influence of that ion on the final properties of the glasses. In particular, short- and mid-range structures were analyzed in terms of the distribution of non bridging oxygen, bridging oxygen, three bridging oxygen species in the glasses, along with the coordination number distribution (cn) and qn species distribution. The results support the hypothesis that the observed changes in the property of the glasses could be directly related to the coordination preferences of the Al ion.     

Structural and Dynamical Properties of a Full-length HIV-1 Integrase: Molecular Dynamics Simulations

Abstract

The structural and dynamical properties of the complete full-length structure of HIV-1 integrase were investigated using Molecular Dynamics approach. Simulations were carried out for the three systems, core domain only (CORE), full-length structure without (FULL) and with a Mg²⁺ (FULL+ION) in its active site, aimed to investigate the difference in the molecular properties of the full-length models due to their different construction procedures as well as the effects of the two ends, C- and N-terminal, on those properties in the core domain. The full-length structure was prepared from the two experimental structures of two-domain fragment. The following properties were observed to differ significantly from the previous reports: (i) relative topology formed by an angle between the three domains; (ii) the cavity size defined by the catalytic triad, Asp64, Asp116, and Glul52; (iii) distances and solvation of the Mg²⁺; and (iv) conformation of the catalytic residues. In addition, the presence of the two terminal domains decreases the mobility of the central core domain significantly.     

Molecular Dynamics Simulations on the Coenzyme Thiamin Diphosphate in Apoenzyme Environment

Thiamin diphosphate (ThDP) is an essential cofactor for a number of enzymes, and especially involved in the nonoxidative decarboxylation of -keto acids by pyruvate decarboxylase (PDC). Recently the crystal structure of PDC bound ThDP has been determined. Based on these X-ray data MD simulations of the isolated coenzyme as well as of ThDP in its enzymatic environment were performed, using the GROMOS87 software package. For the ThDP-apoenzyme modelling all significant amino acid residues with a cut-off radius less than 8.5 Å from the cofactor were taken into account.Because the activity of the coenzyme mainly depends on the formation of a specific structure, the conformational behavior of ThDP and enzyme bound ThDP were investigated within the MD simulations in more detail. Therefore, trajectories of significant structural parameters such as the ring torsion angles _T and _P as well as essential hydrogen bonds were analyzed by our graphics tool. Moreover, Ramachandran-like plots with respect to the torsion angles _T and _P were used for the illustration of preferred orientations of the two aromatic rings in ThDP.Finally, MD simulations on ThDP analogs with less or none catalytic activity and apoenzyme mutants were included, in order to get hints of conformational effects and significant interactions in relation to cofactor-apoenzyme binding and the catalytic mechanism.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s0089460020312     

On the Atomic Velocities in Molecular and Langevin Dynamics Simulations of Soft-Sphere Systems

Abstract

Time dependent probability distributions of the changes of direction of atomic velocities are considered in order to examine in detail the shape of the trajectories obtained through molecular simulations. We have analysed the atomic motions obtained from molecular dynamics simulations of soft-sphere systems at three very different states, i.e. a dilute fluid, a liquid at high density, and a solid. The methodology has also been used to check the reliability of the velocity evolution obtained when it is assumed that a single particle obeys the generalized Langevin equation and the effect of the other particles is represented by friction and random forces.     

Molecular Dynamics as a Mathematical Mapping. III. Efficient Evaluation of the Differentiable Force Functions and Their Derivatives

Abstract

The fully continuous and differentiable framework for performing molecular dynamics calculations introduced in parts I and II of this paper [1,2] requires the evaluation of rather complex force functions and their spatial partial derivatives. This paper presents an efficient interpolation scheme for the evaluation of these quantities over a finite spatial domain.

The modified force function is approximated by a linear combination of Hermite cubic basis functions such that both the interpolant of the force and its spatial derivatives are continuous across the grid boundaries. In order to achieve better accuracy for a given grid size, a nonuniform rectilinear grid is constructed via iterative refinement procedure. The latter guarantees the accuracy of the force computed by interpolation within any specified tolerance > ε O.

For many potential functions of practical interest, it is possible for polynomial interpolants to be constructed for parts of the force functions which are independent of the potential parameters and system density (the so-called “separable force functions”). In such cases, a single interpolation grid which is applicable for a wide range of potential parameters and system densities can be constructed a priori.     

分子动力学模拟与分子生物力学

生物大分子的微观结构动力学决定其生物学功能,其力学-化学耦合规律是分子生物力学的重点关注方向。分子动力学模拟是耦合生物大分子力学-化学性质微观结构动力学基础的有效手段,其结果可用于预测结构-功能关系、指导实验设计和诠释实验结果。本文简要介绍了分子动力学模拟的方法学特点、基本工作原理及其在分子生物力学中的应用,并展望了未来可能的发展方向和应用前景。     

Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions

For the purpose of molecular dynamics simulations of large biopolymers we have developed a new method to accelerate the calculation of long-range pair interactions (e.g. Coulomb interaction). The algorithm introduces distance classes to schedule updates of non-bonding interactions and to avoid unnecessary computations of interactions between particles which are far apart. To minimize the error caused by the updating schedule, the Verlet integration scheme has been modified. The results of the method are compared to those of other approximation schemes as well as to results obtained by numerical integration without approximation. For simulation of a protein with 12 637 atoms our approximation scheme yields a reduction of computer time by a factor of seven. The approximation suggested can be implemented on sequential as well as on parallel computers. We describe an implementation on a (Transputer-based) MIMD machine with a systolic ring architecture.     

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.     

Lipid Membrane Structure and Dynamics Studied by All-Atom Molecular Dynamics Simulations of Hydrated Phospholipid Bilayers

Abstract

The structure and dynamics of phosphatidylcholine bilayers are examined by reviewing the results of several nanoseconds of molecular dynamics simulations on a number of bilayer and monolayer models. The lengths of these simulations, the longest single one of which was 2 nanoseconds, were sufficiently long to effectively sample many of the longer-scale motions governing the behaviour of biomembranes. These simulations reproduce many experimental observables well and provide a degree of resolution currently unavailable experimentally.